LMFDB - Embedded newform 8.14.b.a.5.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8,14,Mod(5,8)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 14, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8.5");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 8 = 2^{3} $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	8.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.57847431615$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{-79}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 20 $ x^2 - x + 20
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			5.1
Root			$0.500000 + 4.44410i$ of defining polynomial
Character	$\chi$	$=$	8.5
Dual form			8.14.b.a.5.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-56.0000 - 71.1056i) q^{2} +2293.15i q^{3} +(-1920.00 + 7963.82i) q^{4} -22576.0i q^{5} +(163056. - 128417. i) q^{6} -175832. q^{7} +(673792. - 309451. i) q^{8} -3.66423e6 q^{9} +O(q^{10})$	\(q+(-56.0000 - 71.1056i) q^{2} +2293.15i q^{3} +(-1920.00 + 7963.82i) q^{4} -22576.0i q^{5} +(163056. - 128417. i) q^{6} -175832. q^{7} +(673792. - 309451. i) q^{8} -3.66423e6 q^{9} +(-1.60528e6 + 1.26426e6i) q^{10} +2.63526e6i q^{11} +(-1.82623e7 - 4.40286e6i) q^{12} -3.10828e7i q^{13} +(9.84659e6 + 1.25026e7i) q^{14} +5.17703e7 q^{15} +(-5.97361e7 - 3.05811e7i) q^{16} -1.33520e8 q^{17} +(2.05197e8 + 2.60547e8i) q^{18} -3.47784e7i q^{19} +(1.79791e8 + 4.33459e7i) q^{20} -4.03210e8i q^{21} +(1.87382e8 - 1.47575e8i) q^{22} -3.55854e7 q^{23} +(7.09620e8 + 1.54511e9i) q^{24} +7.11027e8 q^{25} +(-2.21016e9 + 1.74064e9i) q^{26} -4.74662e9i q^{27} +(3.37597e8 - 1.40029e9i) q^{28} +1.58717e9i q^{29} +(-2.89914e9 - 3.68115e9i) q^{30} -5.76500e9 q^{31} +(1.17074e9 + 5.96011e9i) q^{32} -6.04306e9 q^{33} +(7.47714e9 + 9.49404e9i) q^{34} +3.96959e9i q^{35} +(7.03533e9 - 2.91813e10i) q^{36} +1.31575e10i q^{37} +(-2.47294e9 + 1.94759e9i) q^{38} +7.12777e10 q^{39} +(-6.98618e9 - 1.52115e10i) q^{40} -2.35463e10 q^{41} +(-2.86705e10 + 2.25798e10i) q^{42} +1.45984e10i q^{43} +(-2.09867e10 - 5.05970e9i) q^{44} +8.27238e10i q^{45} +(1.99278e9 + 2.53032e9i) q^{46} -6.81077e10 q^{47} +(7.01271e10 - 1.36984e11i) q^{48} -6.59721e10 q^{49} +(-3.98175e10 - 5.05580e10i) q^{50} -3.06183e11i q^{51} +(2.47538e11 + 5.96790e10i) q^{52} +1.66280e11i q^{53} +(-3.37511e11 + 2.65811e11i) q^{54} +5.94937e10 q^{55} +(-1.18474e11 + 5.44115e10i) q^{56} +7.97523e10 q^{57} +(1.12857e11 - 8.88815e10i) q^{58} -1.27634e11i q^{59} +(-9.93989e10 + 4.12289e11i) q^{60} -4.24164e11i q^{61} +(3.22840e11 + 4.09924e11i) q^{62} +6.44289e11 q^{63} +(3.58236e11 - 4.17012e11i) q^{64} -7.01726e11 q^{65} +(3.38411e11 + 4.29695e11i) q^{66} +3.76204e11i q^{67} +(2.56359e11 - 1.06333e12i) q^{68} -8.16028e10i q^{69} +(2.82260e11 - 2.22297e11i) q^{70} -1.30947e12 q^{71} +(-2.46893e12 + 1.13390e12i) q^{72} +4.78648e11 q^{73} +(9.35572e11 - 7.36820e11i) q^{74} +1.63049e12i q^{75} +(2.76969e11 + 6.67746e10i) q^{76} -4.63363e11i q^{77} +(-3.99155e12 - 5.06824e12i) q^{78} -3.64547e11 q^{79} +(-6.90399e11 + 1.34860e12i) q^{80} +5.04277e12 q^{81} +(1.31860e12 + 1.67428e12i) q^{82} +8.72792e11i q^{83} +(3.21109e12 + 7.74163e11i) q^{84} +3.01436e12i q^{85} +(1.03803e12 - 8.17509e11i) q^{86} -3.63963e12 q^{87} +(8.15485e11 + 1.77562e12i) q^{88} -1.02458e11 q^{89} +(5.88212e12 - 4.63253e12i) q^{90} +5.46536e12i q^{91} +(6.83240e10 - 2.83396e11i) q^{92} -1.32200e13i q^{93} +(3.81403e12 + 4.84284e12i) q^{94} -7.85158e11 q^{95} +(-1.36674e13 + 2.68468e12i) q^{96} -6.15772e12 q^{97} +(3.69444e12 + 4.69098e12i) q^{98} -9.65621e12i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 112 q^{2} - 3840 q^{4} + 326112 q^{6} - 351664 q^{7} + 1347584 q^{8} - 7328466 q^{9}+O(q^{10}) $ 2 * q - 112 * q^2 - 3840 * q^4 + 326112 * q^6 - 351664 * q^7 + 1347584 * q^8 - 7328466 * q^9	\( 2 q - 112 q^{2} - 3840 q^{4} + 326112 q^{6} - 351664 q^{7} + 1347584 q^{8} - 7328466 q^{9} - 3210560 q^{10} - 36524544 q^{12} + 19693184 q^{14} + 103540560 q^{15} - 119472128 q^{16} - 267040604 q^{17} + 410394096 q^{18} + 359582720 q^{20} + 374763360 q^{22} - 71170832 q^{23} + 1419239424 q^{24} + 1422053450 q^{25} - 4420324288 q^{26} + 675194880 q^{28} - 5798271360 q^{30} - 11530003136 q^{31} + 2341470208 q^{32} - 12086118360 q^{33} + 14954273824 q^{34} + 14070654720 q^{36} - 4945877792 q^{38} + 142555458288 q^{39} - 13972357120 q^{40} - 47092697836 q^{41} - 57340925184 q^{42} - 41973496320 q^{44} + 3985566592 q^{46} - 136215473184 q^{47} + 140254248960 q^{48} - 131944236366 q^{49} - 79634993200 q^{50} + 495076320256 q^{52} - 675022489920 q^{54} + 118987366800 q^{55} - 236948389888 q^{56} + 159504558792 q^{57} + 225713203008 q^{58} - 198797875200 q^{60} + 645680175616 q^{62} + 1288578833712 q^{63} + 716471009280 q^{64} - 1403452961440 q^{65} + 676822628160 q^{66} + 512717959680 q^{68} + 564519185920 q^{70} - 2618943314736 q^{71} - 4937861763072 q^{72} + 957295743828 q^{73} + 1871143798976 q^{74} + 553938312704 q^{76} - 7983105664128 q^{78} - 729094463200 q^{79} - 1380797644800 q^{80} + 10085533401402 q^{81} + 2637191078816 q^{82} + 6422183620608 q^{84} + 2076050806112 q^{86} - 7279250797008 q^{87} + 1630970142720 q^{88} - 204915282700 q^{89} + 11764239900480 q^{90} + 136647997440 q^{92} + 7628066498304 q^{94} - 1570316198960 q^{95} - 27334885244928 q^{96} - 12315434746684 q^{97} + 7388877236496 q^{98}+O(q^{100}) \) 2 * q - 112 * q^2 - 3840 * q^4 + 326112 * q^6 - 351664 * q^7 + 1347584 * q^8 - 7328466 * q^9 - 3210560 * q^10 - 36524544 * q^12 + 19693184 * q^14 + 103540560 * q^15 - 119472128 * q^16 - 267040604 * q^17 + 410394096 * q^18 + 359582720 * q^20 + 374763360 * q^22 - 71170832 * q^23 + 1419239424 * q^24 + 1422053450 * q^25 - 4420324288 * q^26 + 675194880 * q^28 - 5798271360 * q^30 - 11530003136 * q^31 + 2341470208 * q^32 - 12086118360 * q^33 + 14954273824 * q^34 + 14070654720 * q^36 - 4945877792 * q^38 + 142555458288 * q^39 - 13972357120 * q^40 - 47092697836 * q^41 - 57340925184 * q^42 - 41973496320 * q^44 + 3985566592 * q^46 - 136215473184 * q^47 + 140254248960 * q^48 - 131944236366 * q^49 - 79634993200 * q^50 + 495076320256 * q^52 - 675022489920 * q^54 + 118987366800 * q^55 - 236948389888 * q^56 + 159504558792 * q^57 + 225713203008 * q^58 - 198797875200 * q^60 + 645680175616 * q^62 + 1288578833712 * q^63 + 716471009280 * q^64 - 1403452961440 * q^65 + 676822628160 * q^66 + 512717959680 * q^68 + 564519185920 * q^70 - 2618943314736 * q^71 - 4937861763072 * q^72 + 957295743828 * q^73 + 1871143798976 * q^74 + 553938312704 * q^76 - 7983105664128 * q^78 - 729094463200 * q^79 - 1380797644800 * q^80 + 10085533401402 * q^81 + 2637191078816 * q^82 + 6422183620608 * q^84 + 2076050806112 * q^86 - 7279250797008 * q^87 + 1630970142720 * q^88 - 204915282700 * q^89 + 11764239900480 * q^90 + 136647997440 * q^92 + 7628066498304 * q^94 - 1570316198960 * q^95 - 27334885244928 * q^96 - 12315434746684 * q^97 + 7388877236496 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/8\mathbb{Z}\right)^\times$.

$n$	$5$	$7$
$\chi(n)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−56.0000	−	71.1056i	−0.618718	−	0.785613i
$2$	−56.0000	−	71.1056i	−0.618718	−	0.785613i
$3$			2293.15i			1.81612i	0.418838	+	0.908061i	$0.362438\pi$
$3$			2293.15i			1.81612i	−0.418838	+	0.908061i	$0.637562\pi$
$4$	−1920.00	+	7963.82i	−0.234375	+	0.972146i
$5$		−	22576.0i		−	0.646163i	−0.946371	−	0.323082i	$-0.895281\pi$
$5$		−	22576.0i		−	0.646163i	0.946371	−	0.323082i	$-0.104719\pi$
$6$	163056.	−	128417.i	1.42677	−	1.12367i
$7$	−175832.			−0.564886			−0.282443	−	0.959284i	$-0.591145\pi$
$7$	−175832.			−0.564886			−0.282443	+	0.959284i	$0.591145\pi$
$8$	673792.	−	309451.i	0.908743	−	0.417357i
$9$	−3.66423e6			−2.29830
$10$	−1.60528e6	+	1.26426e6i	−0.507634	+	0.399793i
$11$			2.63526e6i			0.448509i	0.974531	+	0.224254i	$0.0719947\pi$
$11$			2.63526e6i			0.448509i	−0.974531	+	0.224254i	$0.928005\pi$
$12$	−1.82623e7	−	4.40286e6i	−1.76554	−	0.425654i
$13$		−	3.10828e7i		−	1.78603i	−0.450027	−	0.893015i	$-0.648586\pi$
$13$		−	3.10828e7i		−	1.78603i	0.450027	−	0.893015i	$-0.351414\pi$
$14$	9.84659e6	+	1.25026e7i	0.349505	+	0.443782i
$15$	5.17703e7			1.17351
$16$	−5.97361e7	−	3.05811e7i	−0.890137	−	0.455694i
$17$	−1.33520e8			−1.34162			−0.670810	−	0.741630i	$-0.734053\pi$
$17$	−1.33520e8			−1.34162			−0.670810	+	0.741630i	$0.734053\pi$
$18$	2.05197e8	+	2.60547e8i	1.42200	+	1.80557i
$19$		−	3.47784e7i		−	0.169594i	−0.996398	−	0.0847972i	$-0.972976\pi$
$19$		−	3.47784e7i		−	0.169594i	0.996398	−	0.0847972i	$-0.0270242\pi$
$20$	1.79791e8	+	4.33459e7i	0.628165	+	0.151445i
$21$		−	4.03210e8i		−	1.02590i
$22$	1.87382e8	−	1.47575e8i	0.352354	−	0.277501i
$23$	−3.55854e7			−0.0501235			−0.0250617	−	0.999686i	$-0.507978\pi$
$23$	−3.55854e7			−0.0501235			−0.0250617	+	0.999686i	$0.507978\pi$
$24$	7.09620e8	+	1.54511e9i	0.757971	+	1.65039i
$25$	7.11027e8			0.582473
$26$	−2.21016e9	+	1.74064e9i	−1.40313	+	1.10505i
$27$		−	4.74662e9i		−	2.35787i
$28$	3.37597e8	−	1.40029e9i	0.132395	−	0.549152i
$29$			1.58717e9i			0.495492i	0.968825	+	0.247746i	$0.0796898\pi$
$29$			1.58717e9i			0.495492i	−0.968825	+	0.247746i	$0.920310\pi$
$30$	−2.89914e9	−	3.68115e9i	−0.726073	−	0.921926i
$31$	−5.76500e9			−1.16667			−0.583336	−	0.812231i	$-0.698253\pi$
$31$	−5.76500e9			−1.16667			−0.583336	+	0.812231i	$0.698253\pi$
$32$	1.17074e9	+	5.96011e9i	0.192745	+	0.981249i
$33$	−6.04306e9			−0.814547
$34$	7.47714e9	+	9.49404e9i	0.830085	+	1.05399i
$35$			3.96959e9i			0.365008i
$36$	7.03533e9	−	2.91813e10i	0.538664	−	2.23428i
$37$			1.31575e10i			0.843068i	0.906813	+	0.421534i	$0.138508\pi$
$37$			1.31575e10i			0.843068i	−0.906813	+	0.421534i	$0.861492\pi$
$38$	−2.47294e9	+	1.94759e9i	−0.133236	+	0.104931i
$39$	7.12777e10			3.24365
$40$	−6.98618e9	−	1.52115e10i	−0.269681	−	0.587196i
$41$	−2.35463e10			−0.774156			−0.387078	−	0.922047i	$-0.626516\pi$
$41$	−2.35463e10			−0.774156			−0.387078	+	0.922047i	$0.626516\pi$
$42$	−2.86705e10	+	2.25798e10i	−0.805962	+	0.634744i
$43$			1.45984e10i			0.352176i	0.984374	+	0.176088i	$0.0563443\pi$
$43$			1.45984e10i			0.352176i	−0.984374	+	0.176088i	$0.943656\pi$
$44$	−2.09867e10	−	5.05970e9i	−0.436016	−	0.105119i
$45$			8.27238e10i			1.48508i
$46$	1.99278e9	+	2.53032e9i	0.0310123	+	0.0393776i
$47$	−6.81077e10			−0.921638			−0.460819	−	0.887494i	$-0.652444\pi$
$47$	−6.81077e10			−0.921638			−0.460819	+	0.887494i	$0.652444\pi$
$48$	7.01271e10	−	1.36984e11i	0.827595	−	1.61660i
$49$	−6.59721e10			−0.680904
$50$	−3.98175e10	−	5.05580e10i	−0.360387	−	0.457598i
$51$		−	3.06183e11i		−	2.43654i
$52$	2.47538e11	+	5.96790e10i	1.73628	+	0.418601i
$53$			1.66280e11i			1.03050i	0.857041	+	0.515248i	$0.172300\pi$
$53$			1.66280e11i			1.03050i	−0.857041	+	0.515248i	$0.827700\pi$
$54$	−3.37511e11	+	2.65811e11i	−1.85237	+	1.45886i
$55$	5.94937e10			0.289810
$56$	−1.18474e11	+	5.44115e10i	−0.513336	+	0.235759i
$57$	7.97523e10			0.308004
$58$	1.12857e11	−	8.88815e10i	0.389265	−	0.306570i
$59$		−	1.27634e11i		−	0.393937i	−0.980410	−	0.196969i	$-0.936890\pi$
$59$		−	1.27634e11i		−	0.393937i	0.980410	−	0.196969i	$-0.0631097\pi$
$60$	−9.93989e10	+	4.12289e11i	−0.275042	+	1.14082i
$61$		−	4.24164e11i		−	1.05412i	−0.849828	−	0.527060i	$-0.823294\pi$
$61$		−	4.24164e11i		−	1.05412i	0.849828	−	0.527060i	$-0.176706\pi$
$62$	3.22840e11	+	4.09924e11i	0.721841	+	0.916552i
$63$	6.44289e11			1.29828
$64$	3.58236e11	−	4.17012e11i	0.651627	−	0.758540i
$65$	−7.01726e11			−1.15407
$66$	3.38411e11	+	4.29695e11i	0.503975	+	0.639919i
$67$			3.76204e11i			0.508086i	0.967193	+	0.254043i	$0.0817605\pi$
$67$			3.76204e11i			0.508086i	−0.967193	+	0.254043i	$0.918240\pi$
$68$	2.56359e11	−	1.06333e12i	0.314442	−	1.30425i
$69$		−	8.16028e10i		−	0.0910303i
$70$	2.82260e11	−	2.22297e11i	0.286755	−	0.225837i
$71$	−1.30947e12			−1.21316			−0.606578	−	0.795024i	$-0.707458\pi$
$71$	−1.30947e12			−1.21316			−0.606578	+	0.795024i	$0.707458\pi$
$72$	−2.46893e12	+	1.13390e12i	−2.08856	+	0.959211i
$73$	4.78648e11			0.370184			0.185092	−	0.982721i	$-0.440742\pi$
$73$	4.78648e11			0.370184			0.185092	+	0.982721i	$0.440742\pi$
$74$	9.35572e11	−	7.36820e11i	0.662325	−	0.521622i
$75$			1.63049e12i			1.05784i
$76$	2.76969e11	+	6.67746e10i	0.164871	+	0.0397487i
$77$		−	4.63363e11i		−	0.253356i
$78$	−3.99155e12	−	5.06824e12i	−2.00691	−	2.54825i
$79$	−3.64547e11			−0.168724			−0.0843622	−	0.996435i	$-0.526885\pi$
$79$	−3.64547e11			−0.168724			−0.0843622	+	0.996435i	$0.526885\pi$
$80$	−6.90399e11	+	1.34860e12i	−0.294452	+	0.575174i
$81$	5.04277e12			1.98388
$82$	1.31860e12	+	1.67428e12i	0.478985	+	0.608187i
$83$			8.72792e11i			0.293024i	0.989209	+	0.146512i	$0.0468047\pi$
$83$			8.72792e11i			0.293024i	−0.989209	+	0.146512i	$0.953195\pi$
$84$	3.21109e12	+	7.74163e11i	0.997327	+	0.240446i
$85$			3.01436e12i			0.866905i
$86$	1.03803e12	−	8.17509e11i	0.276674	−	0.217898i
$87$	−3.63963e12			−0.899874
$88$	8.15485e11	+	1.77562e12i	0.187188	+	0.407579i
$89$	−1.02458e11			−0.0218529			−0.0109265	−	0.999940i	$-0.503478\pi$
$89$	−1.02458e11			−0.0218529			−0.0109265	+	0.999940i	$0.503478\pi$
$90$	5.88212e12	−	4.63253e12i	1.16670	−	0.918845i
$91$			5.46536e12i			1.00890i
$92$	6.83240e10	−	2.83396e11i	0.0117477	−	0.0487273i
$93$		−	1.32200e13i		−	2.11882i
$94$	3.81403e12	+	4.84284e12i	0.570234	+	0.724051i
$95$	−7.85158e11			−0.109586
$96$	−1.36674e13	+	2.68468e12i	−1.78207	+	0.350049i
$97$	−6.15772e12			−0.750591			−0.375296	−	0.926905i	$-0.622459\pi$
$97$	−6.15772e12			−0.750591			−0.375296	+	0.926905i	$0.622459\pi$
$98$	3.69444e12	+	4.69098e12i	0.421288	+	0.534927i
$99$		−	9.65621e12i		−	1.03081i
$100$	−1.36517e12	+	5.66249e12i	−0.136517	+	0.566249i
$101$			1.60930e12i			0.150851i	0.997151	+	0.0754255i	$0.0240315\pi$
$101$			1.60930e12i			0.150851i	−0.997151	+	0.0754255i	$0.975968\pi$
$102$	−2.17713e13	+	1.71462e13i	−1.91418	+	1.50754i
$103$	1.98804e13			1.64053			0.820263	−	0.571986i	$-0.193827\pi$
$103$	1.98804e13			1.64053			0.820263	+	0.571986i	$0.193827\pi$
$104$	−9.61863e12	−	2.09434e13i	−0.745412	−	1.62304i
$105$	−9.10287e12			−0.662900
$106$	1.18234e13	−	9.31167e12i	0.809571	−	0.637587i
$107$		−	7.51672e12i		−	0.484210i	−0.970250	−	0.242105i	$-0.922162\pi$
$107$		−	7.51672e12i		−	0.484210i	0.970250	−	0.242105i	$-0.0778379\pi$
$108$	3.78013e13	+	9.11352e12i	2.29220	+	0.552626i
$109$		−	1.41926e13i		−	0.810571i	−0.914190	−	0.405285i	$-0.867172\pi$
$109$		−	1.41926e13i		−	0.810571i	0.914190	−	0.405285i	$-0.132828\pi$
$110$	−3.33165e12	−	4.23033e12i	−0.179311	−	0.227678i
$111$	−3.01722e13			−1.53111
$112$	1.05035e13	+	5.37713e12i	0.502826	+	0.257415i
$113$	2.53739e12			0.114651			0.0573255	−	0.998356i	$-0.481743\pi$
$113$	2.53739e12			0.114651			0.0573255	+	0.998356i	$0.481743\pi$
$114$	−4.46613e12	−	5.67083e12i	−0.190568	−	0.241972i
$115$			8.03377e11i			0.0323879i
$116$	−1.26399e13	−	3.04737e12i	−0.481690	−	0.116131i
$117$			1.13895e14i			4.10483i
$118$	−9.07546e12	+	7.14749e12i	−0.309482	+	0.243736i
$119$	2.34771e13			0.757862
$120$	3.48824e13	−	1.60204e13i	1.06642	−	0.489773i
$121$	2.75781e13			0.798840
$122$	−3.01604e13	+	2.37532e13i	−0.828130	+	0.652203i
$123$		−	5.39954e13i		−	1.40596i
$124$	1.10688e13	−	4.59114e13i	0.273439	−	1.13417i
$125$		−	4.36108e13i		−	1.02254i
$126$	−3.60802e13	−	4.58126e13i	−0.803268	−	1.01994i
$127$	8.19585e13			1.73329			0.866643	−	0.498929i	$-0.166273\pi$
$127$	8.19585e13			1.73329			0.866643	+	0.498929i	$0.166273\pi$
$128$	−4.97130e13	−	2.11988e12i	−0.999092	−	0.0426036i
$129$	−3.34763e13			−0.639594
$130$	3.92967e13	+	4.98967e13i	0.714043	+	0.906650i
$131$			8.80500e13i			1.52218i	0.648646	+	0.761090i	$0.275336\pi$
$131$			8.80500e13i			1.52218i	−0.648646	+	0.761090i	$0.724664\pi$
$132$	1.16027e13	−	4.81258e13i	0.190909	−	0.791859i
$133$			6.11516e12i			0.0958015i
$134$	2.67502e13	−	2.10674e13i	0.399159	−	0.314362i
$135$	−1.07160e14			−1.52357
$136$	−8.99649e13	+	4.13180e13i	−1.21919	+	0.559934i
$137$	−1.32282e14			−1.70929			−0.854647	−	0.519210i	$-0.826226\pi$
$137$	−1.32282e14			−1.70929			−0.854647	+	0.519210i	$0.826226\pi$
$138$	−5.80242e12	+	4.56976e12i	−0.0715146	+	0.0563222i
$139$			1.56396e13i			0.183920i	0.995763	+	0.0919598i	$0.0293131\pi$
$139$			1.56396e13i			0.183920i	−0.995763	+	0.0919598i	$0.970687\pi$
$140$	−3.16131e13	−	7.62160e12i	−0.354842	−	0.0855488i
$141$		−	1.56182e14i		−	1.67381i
$142$	7.33304e13	+	9.31107e13i	0.750602	+	0.953071i
$143$	8.19114e13			0.801051
$144$	2.18887e14	+	1.12056e14i	2.04580	+	1.04732i
$145$	3.58320e13			0.320169
$146$	−2.68043e13	−	3.40345e13i	−0.229040	−	0.290821i
$147$		−	1.51284e14i		−	1.23661i
$148$	−1.04784e14	−	2.52624e13i	−0.819585	−	0.197594i
$149$			8.86015e13i			0.663331i	0.943397	+	0.331665i	$0.107610\pi$
$149$			8.86015e13i			0.663331i	−0.943397	+	0.331665i	$0.892390\pi$
$150$	1.15937e14	−	9.13077e13i	0.831055	−	0.654507i
$151$	−8.60856e13			−0.590990			−0.295495	−	0.955344i	$-0.595485\pi$
$151$	−8.60856e13			−0.590990			−0.295495	+	0.955344i	$0.595485\pi$
$152$	−1.07622e13	−	2.34334e13i	−0.0707814	−	0.154118i
$153$	4.89249e14			3.08344
$154$	−3.29477e13	+	2.59483e13i	−0.199040	+	0.156756i
$155$			1.30151e14i			0.753860i
$156$	−1.36853e14	+	5.67643e14i	−0.760230	+	3.15330i
$157$		−	2.50929e14i		−	1.33722i	−0.743612	−	0.668612i	$-0.766889\pi$
$157$		−	2.50929e14i		−	1.33722i	0.743612	−	0.668612i	$-0.233111\pi$
$158$	2.04146e13	+	2.59213e13i	0.104393	+	0.132552i
$159$	−3.81305e14			−1.87151
$160$	1.34555e14	−	2.64305e13i	0.634047	−	0.124545i
$161$	6.25705e12			0.0283140
$162$	−2.82395e14	−	3.58569e14i	−1.22747	−	1.55856i
$163$			1.10826e14i			0.462832i	0.972855	+	0.231416i	$0.0743359\pi$
$163$			1.10826e14i			0.462832i	−0.972855	+	0.231416i	$0.925664\pi$
$164$	4.52090e13	−	1.87519e14i	0.181443	−	0.752593i
$165$			1.36428e14i			0.526330i
$166$	6.20604e13	−	4.88764e13i	0.230203	−	0.181299i
$167$	2.20904e14			0.788038			0.394019	−	0.919102i	$-0.371084\pi$
$167$	2.20904e14			0.788038			0.394019	+	0.919102i	$0.371084\pi$
$168$	−1.24774e14	−	2.71680e14i	−0.428167	−	0.932281i
$169$	−6.63267e14			−2.18990
$170$	2.14337e14	−	1.68804e14i	0.681052	−	0.536370i
$171$			1.27436e14i			0.389779i
$172$	−1.16259e14	−	2.80289e13i	−0.342366	−	0.0825412i
$173$			1.06956e14i			0.303323i	0.988432	+	0.151662i	$0.0484624\pi$
$173$			1.06956e14i			0.303323i	−0.988432	+	0.151662i	$0.951538\pi$
$174$	2.03819e14	+	2.58798e14i	0.556768	+	0.706952i
$175$	−1.25021e14			−0.329031
$176$	8.05891e13	−	1.57420e14i	0.204383	−	0.399234i
$177$	2.92684e14			0.715439
$178$	5.73763e12	+	7.28531e12i	0.0135208	+	0.0171679i
$179$			5.93686e14i			1.34900i	0.738274	+	0.674501i	$0.235641\pi$
$179$			5.93686e14i			1.34900i	−0.738274	+	0.674501i	$0.764359\pi$
$180$	−6.58797e14	−	1.58830e14i	−1.44371	−	0.348065i
$181$		−	3.90359e14i		−	0.825188i	−0.910915	−	0.412594i	$-0.864623\pi$
$181$		−	3.90359e14i		−	0.825188i	0.910915	−	0.412594i	$-0.135377\pi$
$182$	3.88617e14	−	3.06060e14i	0.792607	−	0.624227i
$183$	9.72673e14			1.91441
$184$	−2.39772e13	+	1.10120e13i	−0.0455493	+	0.0209194i
$185$	2.97044e14			0.544759
$186$	−9.40018e14	+	7.40322e14i	−1.66457	+	1.31095i
$187$		−	3.51861e14i		−	0.601728i
$188$	1.30767e14	−	5.42398e14i	0.216009	−	0.895967i
$189$			8.34608e14i			1.33193i
$190$	4.39689e13	+	5.58291e13i	0.0678027	+	0.0860919i
$191$	1.05717e14			0.157553			0.0787764	−	0.996892i	$-0.474899\pi$
$191$	1.05717e14			0.157553			0.0787764	+	0.996892i	$0.474899\pi$
$192$	9.56272e14	+	8.21489e14i	1.37760	+	1.18343i
$193$	−3.84017e14			−0.534844			−0.267422	−	0.963579i	$-0.586172\pi$
$193$	−3.84017e14			−0.534844			−0.267422	+	0.963579i	$0.586172\pi$
$194$	3.44832e14	+	4.37848e14i	0.464405	+	0.589674i
$195$		−	1.60917e15i		−	2.09593i
$196$	1.26666e14	−	5.25390e14i	0.159587	−	0.661938i
$197$			4.39842e14i			0.536125i	0.963401	+	0.268063i	$0.0863834\pi$
$197$			4.39842e14i			0.536125i	−0.963401	+	0.268063i	$0.913617\pi$
$198$	−6.86610e14	+	5.40748e14i	−0.809816	+	0.637780i
$199$	−1.15322e15			−1.31634			−0.658171	−	0.752868i	$-0.728670\pi$
$199$	−1.15322e15			−1.31634			−0.658171	+	0.752868i	$0.728670\pi$
$200$	4.79084e14	−	2.20028e14i	0.529318	−	0.243099i
$201$	−8.62694e14			−0.922746
$202$	1.14430e14	−	9.01208e13i	0.118510	−	0.0933343i
$203$		−	2.79075e14i		−	0.279896i
$204$	2.43838e15	+	5.87871e14i	2.36868	+	0.571065i
$205$			5.31583e14i			0.500231i
$206$	−1.11330e15	−	1.41361e15i	−1.01502	−	1.28882i
$207$	1.30393e14			0.115199
$208$	−9.50547e14	+	1.85677e15i	−0.813882	+	1.58981i
$209$	9.16502e13			0.0760646
$210$	5.09761e14	+	6.47265e14i	0.410148	+	0.520783i
$211$		−	1.61545e15i		−	1.26025i	−0.776494	−	0.630125i	$-0.783004\pi$
$211$		−	1.61545e15i		−	1.26025i	0.776494	−	0.630125i	$-0.216996\pi$
$212$	−1.32422e15	−	3.19257e14i	−1.00179	−	0.241522i
$213$		−	3.00282e15i		−	2.20324i
$214$	−5.34481e14	+	4.20936e14i	−0.380402	+	0.299590i
$215$	3.29573e14			0.227563
$216$	−1.46885e15	−	3.19824e15i	−0.984074	−	2.14270i
$217$	1.01367e15			0.659036
$218$	−1.00918e15	+	7.94788e14i	−0.636795	+	0.501515i
$219$			1.09761e15i			0.672299i
$220$	−1.14228e14	+	4.73797e14i	−0.0679242	+	0.281738i
$221$			4.15019e15i			2.39617i
$222$	1.68964e15	+	2.14541e15i	0.947328	+	1.20286i
$223$	1.76111e15			0.958970			0.479485	−	0.877550i	$-0.340824\pi$
$223$	1.76111e15			0.958970			0.479485	+	0.877550i	$0.340824\pi$
$224$	−2.05853e14	−	1.04798e15i	−0.108879	−	0.554294i
$225$	−2.60537e15			−1.33870
$226$	−1.42094e14	−	1.80423e14i	−0.0709367	−	0.0900713i
$227$			3.50680e15i			1.70115i	0.525852	+	0.850576i	$0.323747\pi$
$227$			3.50680e15i			1.70115i	−0.525852	+	0.850576i	$0.676253\pi$
$228$	−1.53124e14	+	6.35133e14i	−0.0721885	+	0.299425i
$229$		−	2.96284e15i		−	1.35762i	−0.734315	−	0.678808i	$-0.762497\pi$
$229$		−	2.96284e15i		−	1.35762i	0.734315	−	0.678808i	$-0.237503\pi$
$230$	5.71246e13	−	4.49891e13i	0.0254444	−	0.0200390i
$231$	1.06256e15			0.460126
$232$	4.91152e14	+	1.06942e15i	0.206797	+	0.450275i
$233$	1.85883e15			0.761073			0.380536	−	0.924766i	$-0.375739\pi$
$233$	1.85883e15			0.761073			0.380536	+	0.924766i	$0.375739\pi$
$234$	8.09855e15	−	6.37811e15i	3.22481	−	2.53974i
$235$			1.53760e15i			0.595529i
$236$	1.01645e15	+	2.45057e14i	0.382965	+	0.0923291i
$237$		−	8.35963e14i		−	0.306424i
$238$	−1.31472e15	−	1.66936e15i	−0.468903	−	0.595386i
$239$	−3.71990e15			−1.29105			−0.645527	−	0.763737i	$-0.723362\pi$
$239$	−3.71990e15			−1.29105			−0.645527	+	0.763737i	$0.723362\pi$
$240$	−3.09255e15	−	1.58319e15i	−1.04459	−	0.534762i
$241$	3.83441e15			1.26063			0.630316	−	0.776339i	$-0.282925\pi$
$241$	3.83441e15			1.26063			0.630316	+	0.776339i	$0.282925\pi$
$242$	−1.54437e15	−	1.96096e15i	−0.494257	−	0.627579i
$243$			3.99619e15i			1.24510i
$244$	3.37797e15	+	8.14395e14i	1.02476	+	0.247059i
$245$			1.48939e15i			0.439975i
$246$	−3.83937e15	+	3.02374e15i	−1.10454	+	0.869895i
$247$	−1.08101e15			−0.302901
$248$	−3.88441e15	+	1.78399e15i	−1.06020	+	0.486918i
$249$	−2.00145e15			−0.532168
$250$	−3.10097e15	+	2.44220e15i	−0.803317	+	0.632662i
$251$		−	5.75804e15i		−	1.45343i	−0.686937	−	0.726717i	$-0.741045\pi$
$251$		−	5.75804e15i		−	1.45343i	0.686937	−	0.726717i	$-0.258955\pi$
$252$	−1.23704e15	+	5.13101e15i	−0.304284	+	1.26212i
$253$		−	9.37769e13i		−	0.0224808i
$254$	−4.58968e15	−	5.82771e15i	−1.07242	−	1.36169i
$255$	−6.91238e15			−1.57441
$256$	2.63320e15	+	3.65359e15i	0.584687	+	0.811259i
$257$	5.36913e15			1.16235			0.581177	−	0.813777i	$-0.302592\pi$
$257$	5.36913e15			1.16235			0.581177	+	0.813777i	$0.302592\pi$
$258$	1.87467e15	+	2.38035e15i	0.395729	+	0.502473i
$259$		−	2.31351e15i		−	0.476237i
$260$	1.34731e15	−	5.58842e15i	0.270484	−	1.12192i
$261$		−	5.81576e15i		−	1.13879i
$262$	6.26085e15	−	4.93080e15i	1.19584	−	0.941801i
$263$	5.06713e15			0.944169			0.472085	−	0.881553i	$-0.343502\pi$
$263$	5.06713e15			0.944169			0.472085	+	0.881553i	$0.343502\pi$
$264$	−4.07176e15	+	1.87003e15i	−0.740214	+	0.339957i
$265$	3.75393e15			0.665868
$266$	4.34822e14	−	3.42449e14i	0.0752629	−	0.0592741i
$267$		−	2.34951e14i		−	0.0396876i
$268$	−2.99602e15	−	7.22312e14i	−0.493934	−	0.119083i
$269$		−	3.17366e15i		−	0.510705i	−0.966848	−	0.255352i	$-0.917809\pi$
$269$		−	3.17366e15i		−	0.510705i	0.966848	−	0.255352i	$-0.0821915\pi$
$270$	6.00095e15	+	7.61966e15i	0.942661	+	1.19694i
$271$	−7.50971e15			−1.15166			−0.575828	−	0.817571i	$-0.695320\pi$
$271$	−7.50971e15			−1.15166			−0.575828	+	0.817571i	$0.695320\pi$
$272$	7.97598e15	+	4.08319e15i	1.19422	+	0.611367i
$273$	−1.25329e16			−1.83229
$274$	7.40779e15	+	9.40598e15i	1.05757	+	1.34284i
$275$			1.87374e15i			0.261244i
$276$	6.49871e14	+	1.56677e14i	0.0884948	+	0.0213352i
$277$			4.46002e15i			0.593223i	0.954998	+	0.296611i	$0.0958566\pi$
$277$			4.46002e15i			0.593223i	−0.954998	+	0.296611i	$0.904143\pi$
$278$	1.11206e15	−	8.75815e14i	0.144490	−	0.113794i
$279$	2.11243e16			2.68136
$280$	1.22839e15	+	2.67468e15i	0.152339	+	0.331699i
$281$	−1.31980e16			−1.59926			−0.799628	−	0.600496i	$-0.794970\pi$
$281$	−1.31980e16			−1.59926			−0.799628	+	0.600496i	$0.794970\pi$
$282$	−1.11054e16	+	8.74617e15i	−1.31496	+	1.03562i
$283$			5.42208e15i			0.627413i	0.949520	+	0.313707i	$0.101571\pi$
$283$			5.42208e15i			0.627413i	−0.949520	+	0.313707i	$0.898429\pi$
$284$	2.51419e15	−	1.04284e16i	0.284334	−	1.17937i
$285$		−	1.80049e15i		−	0.199021i
$286$	−4.58704e15	−	5.82435e15i	−0.495625	−	0.629316i
$287$	4.14020e15			0.437310
$288$	−4.28985e15	−	2.18392e16i	−0.442987	−	2.25520i
$289$	7.92309e15			0.799943
$290$	−2.00659e15	−	2.54785e15i	−0.198094	−	0.251529i
$291$		−	1.41206e16i		−	1.36317i
$292$	−9.19004e14	+	3.81187e15i	−0.0867619	+	0.359873i
$293$			1.34705e16i			1.24378i	0.783104	+	0.621891i	$0.213635\pi$
$293$			1.34705e16i			1.24378i	−0.783104	+	0.621891i	$0.786365\pi$
$294$	−1.07571e16	+	8.47192e15i	−0.971493	+	0.765110i
$295$	−2.88146e15			−0.254548
$296$	4.07161e15	+	8.86542e15i	0.351860	+	0.766132i
$297$	1.25086e16			1.05753
$298$	6.30006e15	−	4.96168e15i	0.521121	−	0.410415i
$299$			1.10610e15i			0.0895220i
$300$	−1.29850e16	−	3.13055e15i	−1.02838	−	0.247932i
$301$		−	2.56686e15i		−	0.198939i
$302$	4.82079e15	+	6.12116e15i	0.365657	+	0.464290i
$303$	−3.69037e15			−0.273964
$304$	−1.06356e15	+	2.07753e15i	−0.0772831	+	0.150962i
$305$	−9.57593e15			−0.681133
$306$	−2.73980e16	−	3.47884e16i	−1.90778	−	2.42239i
$307$		−	1.70291e15i		−	0.116089i	−0.998314	−	0.0580447i	$-0.981513\pi$
$307$		−	1.70291e15i		−	0.116089i	0.998314	−	0.0580447i	$-0.0184866\pi$
$308$	3.69014e15	+	8.89657e14i	0.246299	+	0.0593804i
$309$			4.55888e16i			2.97940i
$310$	9.25444e15	−	7.28844e15i	0.592242	−	0.466427i
$311$	−1.66557e16			−1.04381			−0.521903	−	0.853005i	$-0.674778\pi$
$311$	−1.66557e16			−1.04381			−0.521903	+	0.853005i	$0.674778\pi$
$312$	4.80264e16	−	2.20570e16i	2.94764	−	1.35376i
$313$	−1.38291e16			−0.831294			−0.415647	−	0.909526i	$-0.636445\pi$
$313$	−1.38291e16			−0.831294			−0.415647	+	0.909526i	$0.636445\pi$
$314$	−1.78425e16	+	1.40521e16i	−1.05054	+	0.827365i
$315$		−	1.45455e16i		−	0.838899i
$316$	6.99931e14	−	2.90319e15i	0.0395448	−	0.164025i
$317$		−	1.12001e16i		−	0.619923i	−0.950749	−	0.309962i	$-0.899684\pi$
$317$		−	1.12001e16i		−	0.619923i	0.950749	−	0.309962i	$-0.100316\pi$
$318$	2.13531e16	+	2.71129e16i	1.15794	+	1.47028i
$319$	−4.18261e15			−0.222233
$320$	−9.41446e15	−	8.08753e15i	−0.490141	−	0.421057i
$321$	1.72370e16			0.879385
$322$	−3.50395e14	−	4.44911e14i	−0.0175184	−	0.0222439i
$323$			4.64363e15i			0.227531i
$324$	−9.68211e15	+	4.01597e16i	−0.464973	+	1.92863i
$325$		−	2.21007e16i		−	1.04031i
$326$	7.88037e15	−	6.20628e15i	0.363607	−	0.286363i
$327$	3.25459e16			1.47210
$328$	−1.58653e16	+	7.28645e15i	−0.703509	+	0.323099i
$329$	1.19755e16			0.520620
$330$	9.70080e15	−	7.63998e15i	0.413492	−	0.325650i
$331$			4.12308e16i			1.72322i	0.507574	+	0.861608i	$0.330542\pi$
$331$			4.12308e16i			1.72322i	−0.507574	+	0.861608i	$0.669458\pi$
$332$	−6.95076e15	−	1.67576e15i	−0.284862	−	0.0686775i
$333$		−	4.82122e16i		−	1.93762i
$334$	−1.23706e16	−	1.57075e16i	−0.487573	−	0.619093i
$335$	8.49319e15			0.328307
$336$	−1.23306e16	+	2.40862e16i	−0.467497	+	0.913193i
$337$	−6.12744e15			−0.227869			−0.113934	−	0.993488i	$-0.536345\pi$
$337$	−6.12744e15			−0.227869			−0.113934	+	0.993488i	$0.536345\pi$
$338$	3.71430e16	+	4.71620e16i	1.35493	+	1.72042i
$339$			5.81863e15i			0.208220i
$340$	−2.40058e16	−	5.78756e15i	−0.842759	−	0.203181i
$341$		−	1.51923e16i		−	0.523262i
$342$	9.06142e15	−	7.13643e15i	0.306215	−	0.241163i
$343$	2.86362e16			0.949519
$344$	4.51749e15	+	9.83627e15i	0.146983	+	0.320037i
$345$	−1.84227e15			−0.0588205
$346$	7.60517e15	−	5.98954e15i	0.238295	−	0.187672i
$347$		−	5.59292e16i		−	1.71987i	−0.510400	−	0.859937i	$-0.670503\pi$
$347$		−	5.59292e16i		−	1.71987i	0.510400	−	0.859937i	$-0.329497\pi$
$348$	6.98808e15	−	2.89853e16i	0.210908	−	0.874809i
$349$		−	2.97671e16i		−	0.881802i	−0.897556	−	0.440901i	$-0.854659\pi$
$349$		−	2.97671e16i		−	0.881802i	0.897556	−	0.440901i	$-0.145341\pi$
$350$	7.00119e15	+	8.88971e15i	0.203577	+	0.258491i
$351$	−1.47538e17			−4.21123
$352$	−1.57064e16	+	3.08519e15i	−0.440099	+	0.0864480i
$353$	−4.62642e16			−1.27265			−0.636326	−	0.771420i	$-0.719547\pi$
$353$	−4.62642e16			−1.27265			−0.636326	+	0.771420i	$0.719547\pi$
$354$	−1.63903e16	−	2.08114e16i	−0.442655	−	0.562058i
$355$			2.95627e16i			0.783897i
$356$	1.96719e14	−	8.15954e14i	0.00512178	−	0.0212442i
$357$			5.38367e16i			1.37637i
$358$	4.22144e16	−	3.32464e16i	1.05979	−	0.834652i
$359$	5.67385e16			1.39883			0.699414	−	0.714717i	$-0.253445\pi$
$359$	5.67385e16			1.39883			0.699414	+	0.714717i	$0.253445\pi$
$360$	2.55990e16	+	5.57386e16i	0.619807	+	1.34955i
$361$	4.08434e16			0.971238
$362$	−2.77567e16	+	2.18601e16i	−0.648279	+	0.510559i
$363$			6.32409e16i			1.45079i
$364$	−4.35251e16	−	1.04935e16i	−0.980801	−	0.236462i
$365$		−	1.08060e16i		−	0.239199i
$366$	−5.44697e16	−	6.91625e16i	−1.18448	−	1.50398i
$367$	−8.60952e16			−1.83929			−0.919644	−	0.392754i	$-0.871522\pi$
$367$	−8.60952e16			−1.83929			−0.919644	+	0.392754i	$0.871522\pi$
$368$	2.12573e15	+	1.08824e15i	0.0446167	+	0.0228409i
$369$	8.62793e16			1.77924
$370$	−1.66345e16	−	2.11215e16i	−0.337053	−	0.427970i
$371$		−	2.92373e16i		−	0.582112i
$372$	1.05282e17	+	2.53825e16i	2.05980	+	0.496598i
$373$		−	5.12559e16i		−	0.985454i	−0.870184	−	0.492727i	$-0.836000\pi$
$373$		−	5.12559e16i		−	0.985454i	0.870184	−	0.492727i	$-0.164000\pi$
$374$	−2.50193e16	+	1.97042e16i	−0.472725	+	0.372300i
$375$	1.00006e17			1.85705
$376$	−4.58904e16	+	2.10760e16i	−0.837532	+	0.384652i
$377$	4.93337e16			0.884963
$378$	5.93453e16	−	4.67381e16i	1.04638	−	0.824089i
$379$			1.33591e16i			0.231537i	0.993276	+	0.115769i	$0.0369331\pi$
$379$			1.33591e16i			0.231537i	−0.993276	+	0.115769i	$0.963067\pi$
$380$	1.50750e15	−	6.25286e15i	0.0256841	−	0.106533i
$381$			1.87944e17i			3.14786i
$382$	−5.92013e15	−	7.51704e15i	−0.0974808	−	0.123776i
$383$	6.66216e16			1.07851			0.539254	−	0.842143i	$-0.318706\pi$
$383$	6.66216e16			1.07851			0.539254	+	0.842143i	$0.318706\pi$
$384$	4.86121e15	−	1.14000e17i	0.0773733	−	1.81447i
$385$	−1.04609e16			−0.163710
$386$	2.15049e16	+	2.73057e16i	0.330918	+	0.420181i
$387$		−	5.34918e16i		−	0.809406i
$388$	1.18228e16	−	4.90390e16i	0.175920	−	0.729684i
$389$		−	2.50535e16i		−	0.366603i	−0.983057	−	0.183302i	$-0.941321\pi$
$389$		−	2.50535e16i		−	0.366603i	0.983057	−	0.183302i	$-0.0586785\pi$
$390$	−1.14421e17	+	9.01134e16i	−1.64659	+	1.29679i
$391$	4.75138e15			0.0672466
$392$	−4.44515e16	+	2.04152e16i	−0.618767	+	0.284180i
$393$	−2.01912e17			−2.76447
$394$	3.12752e16	−	2.46312e16i	0.421187	−	0.331711i
$395$			8.23002e15i			0.109023i
$396$	7.69003e16	+	1.85399e16i	1.00210	+	0.241596i
$397$			3.42600e15i			0.0439186i	0.999759	+	0.0219593i	$0.00699043\pi$
$397$			3.42600e15i			0.0439186i	−0.999759	+	0.0219593i	$0.993010\pi$
$398$	6.45806e16	+	8.20007e16i	0.814446	+	1.03414i
$399$	−1.40230e16			−0.173987
$400$	−4.24739e16	−	2.17440e16i	−0.518481	−	0.265429i
$401$	−6.31120e16			−0.758007			−0.379004	−	0.925395i	$-0.623733\pi$
$401$	−6.31120e16			−0.758007			−0.379004	+	0.925395i	$0.623733\pi$
$402$	4.83109e16	+	6.13423e16i	0.570920	+	0.724921i
$403$			1.79193e17i			2.08371i
$404$	−1.28162e16	−	3.08986e15i	−0.146649	−	0.0353557i
$405$		−	1.13846e17i		−	1.28191i
$406$	−1.98438e16	+	1.56282e16i	−0.219890	+	0.173177i
$407$	−3.46735e16			−0.378123
$408$	−9.47486e16	−	2.06303e17i	−1.01691	−	2.21419i
$409$	4.68238e16			0.494613			0.247306	−	0.968937i	$-0.420455\pi$
$409$	4.68238e16			0.494613			0.247306	+	0.968937i	$0.420455\pi$
$410$	3.77985e16	−	2.97686e16i	0.392988	−	0.309502i
$411$		−	3.03343e17i		−	3.10429i
$412$	−3.81704e16	+	1.58324e17i	−0.384498	+	1.59483i
$413$			2.24421e16i			0.222530i
$414$	−7.30202e15	−	9.27168e15i	−0.0712756	−	0.0905016i
$415$	1.97042e16			0.189341
$416$	1.85257e17	−	3.63898e16i	1.75254	−	0.344249i
$417$	−3.58639e16			−0.334021
$418$	−5.13241e15	−	6.51684e15i	−0.0470626	−	0.0597573i
$419$		−	1.77223e17i		−	1.60003i	−0.599977	−	0.800017i	$-0.704824\pi$
$419$		−	1.77223e17i		−	1.60003i	0.599977	−	0.800017i	$-0.295176\pi$
$420$	1.74775e16	−	7.24937e16i	0.155367	−	0.644436i
$421$		−	4.62012e16i		−	0.404408i	−0.979343	−	0.202204i	$-0.935190\pi$
$421$		−	4.62012e16i		−	0.404408i	0.979343	−	0.202204i	$-0.0648104\pi$
$422$	−1.14867e17	+	9.04651e16i	−0.990069	+	0.779740i
$423$	2.49563e17			2.11820
$424$	5.14555e16	+	1.12038e17i	0.430084	+	0.936455i
$425$	−9.49365e16			−0.781457
$426$	−2.13517e17	+	1.68158e17i	−1.73089	+	1.36319i
$427$			7.45816e16i			0.595457i
$428$	5.98618e16	+	1.44321e16i	0.470723	+	0.113487i
$429$			1.87835e17i			1.45481i
$430$	−1.84561e16	−	2.34345e16i	−0.140797	−	0.178776i
$431$	−1.48095e17			−1.11285			−0.556427	−	0.830896i	$-0.687828\pi$
$431$	−1.48095e17			−1.11285			−0.556427	+	0.830896i	$0.687828\pi$
$432$	−1.45157e17	+	2.83545e17i	−1.07447	+	2.09883i
$433$	1.84376e17			1.34442			0.672208	−	0.740362i	$-0.265346\pi$
$433$	1.84376e17			1.34442			0.672208	+	0.740362i	$0.265346\pi$
$434$	−5.67656e16	−	7.20777e16i	−0.407758	−	0.517747i
$435$			8.21682e16i			0.581465i
$436$	1.13028e17	+	2.72499e16i	0.787994	+	0.189978i
$437$			1.23760e15i			0.00850066i
$438$	7.80464e16	−	6.14663e16i	0.528167	−	0.415964i
$439$	−1.46084e17			−0.974052			−0.487026	−	0.873388i	$-0.661918\pi$
$439$	−1.46084e17			−0.974052			−0.487026	+	0.873388i	$0.661918\pi$
$440$	4.00864e16	−	1.84104e16i	0.263363	−	0.120954i
$441$	2.41737e17			1.56492
$442$	2.95102e17	−	2.32411e17i	1.88246	−	1.48256i
$443$		−	3.72026e16i		−	0.233856i	−0.993140	−	0.116928i	$-0.962695\pi$
$443$		−	3.72026e16i		−	0.233856i	0.993140	−	0.116928i	$-0.0373047\pi$
$444$	5.79306e16	−	2.40286e17i	0.358855	−	1.48847i
$445$			2.31309e15i			0.0141205i
$446$	−9.86222e16	−	1.25225e17i	−0.593332	−	0.753379i
$447$	−2.03177e17			−1.20469
$448$	−6.29893e16	+	7.33240e16i	−0.368095	+	0.428488i
$449$	−1.18166e17			−0.680597			−0.340299	−	0.940317i	$-0.610528\pi$
$449$	−1.18166e17			−0.680597			−0.340299	+	0.940317i	$0.610528\pi$
$450$	1.45901e17	+	1.85256e17i	0.828277	+	1.05170i
$451$		−	6.20508e16i		−	0.347216i
$452$	−4.87179e15	+	2.02073e16i	−0.0268713	+	0.111457i
$453$		−	1.97408e17i		−	1.07331i
$454$	2.49353e17	−	1.96381e17i	1.33645	−	1.05253i
$455$	1.23386e17			0.651916
$456$	5.37364e16	−	2.46795e16i	0.279897	−	0.128548i
$457$	1.23578e17			0.634578			0.317289	−	0.948329i	$-0.397228\pi$
$457$	1.23578e17			0.634578			0.317289	+	0.948329i	$0.397228\pi$
$458$	−2.10674e17	+	1.65919e17i	−1.06656	+	0.839982i
$459$			6.33770e17i			3.16337i
$460$	−6.39795e15	−	1.54248e15i	−0.0314858	−	0.00759092i
$461$			2.12255e17i			1.02992i	0.857215	+	0.514959i	$0.172193\pi$
$461$			2.12255e17i			1.02992i	−0.857215	+	0.514959i	$0.827807\pi$
$462$	−5.95035e16	−	7.55541e16i	−0.284689	−	0.361481i
$463$	−1.34235e17			−0.633273			−0.316636	−	0.948547i	$-0.602553\pi$
$463$	−1.34235e17			−0.633273			−0.316636	+	0.948547i	$0.602553\pi$
$464$	4.85374e16	−	9.48113e16i	0.225792	−	0.441055i
$465$	−2.98456e17			−1.36910
$466$	−1.04094e17	−	1.32173e17i	−0.470890	−	0.597909i
$467$		−	8.38926e15i		−	0.0374252i	−0.999825	−	0.0187126i	$-0.994043\pi$
$467$		−	8.38926e15i		−	0.0374252i	0.999825	−	0.0187126i	$-0.00595675\pi$
$468$	−9.07037e17	−	2.18678e17i	−3.99050	−	0.962070i
$469$		−	6.61487e16i		−	0.287011i
$470$	1.09332e17	−	8.61057e16i	0.467855	−	0.368465i
$471$	5.75420e17			2.42856
$472$	−3.94964e16	−	8.59986e16i	−0.164412	−	0.357988i
$473$	−3.84705e16			−0.157954
$474$	−5.94416e16	+	4.68139e16i	−0.240731	+	0.189590i
$475$		−	2.47284e16i		−	0.0987842i
$476$	−4.50761e16	+	1.86968e17i	−0.177624	+	0.736752i
$477$		−	6.09288e17i		−	2.36839i
$478$	2.08314e17	+	2.64505e17i	0.798799	+	1.01427i
$479$	−2.32521e17			−0.879591			−0.439795	−	0.898098i	$-0.644949\pi$
$479$	−2.32521e17			−0.879591			−0.439795	+	0.898098i	$0.644949\pi$
$480$	6.06093e16	+	3.08556e17i	0.226189	+	1.15151i
$481$	4.08973e17			1.50574
$482$	−2.14727e17	−	2.72648e17i	−0.779976	−	0.990368i
$483$			1.43484e16i			0.0514218i
$484$	−5.29500e16	+	2.19627e17i	−0.187228	+	0.776589i
$485$			1.39017e17i			0.485004i
$486$	2.84151e17	−	2.23787e17i	0.978169	−	0.770369i
$487$	−2.79560e17			−0.949591			−0.474795	−	0.880096i	$-0.657478\pi$
$487$	−2.79560e17			−0.949591			−0.474795	+	0.880096i	$0.657478\pi$
$488$	−1.31258e17	−	2.85798e17i	−0.439944	−	0.957923i
$489$	−2.54142e17			−0.840560
$490$	1.05904e17	−	8.34057e16i	0.345650	−	0.272221i
$491$			3.29017e17i			1.05971i	0.848087	+	0.529856i	$0.177754\pi$
$491$			3.29017e17i			1.05971i	−0.848087	+	0.529856i	$0.822246\pi$
$492$	4.30010e17	+	1.03671e17i	1.36680	+	0.329522i
$493$		−	2.11919e17i		−	0.664761i
$494$	6.05367e16	+	7.68659e16i	0.187410	+	0.237963i
$495$	−2.17999e17			−0.666070
$496$	3.44379e17	+	1.76300e17i	1.03850	+	0.531644i
$497$	2.30247e17			0.685295
$498$	1.12081e17	+	1.42314e17i	0.329262	+	0.418078i
$499$			1.20530e17i			0.349495i	0.984613	+	0.174748i	$0.0559110\pi$
$499$			1.20530e17i			0.349495i	−0.984613	+	0.174748i	$0.944089\pi$
$500$	3.47308e17	+	8.37327e16i	0.994054	+	0.239657i
$501$			5.06568e17i			1.43117i
$502$	−4.09429e17	+	3.22450e17i	−1.14184	+	0.899267i
$503$	1.54881e17			0.426388			0.213194	−	0.977010i	$-0.431613\pi$
$503$	1.54881e17			0.426388			0.213194	+	0.977010i	$0.431613\pi$
$504$	4.34117e17	−	1.99376e17i	1.17980	−	0.541845i
$505$	3.63316e16			0.0974744
$506$	−6.66806e15	+	5.25150e15i	−0.0176612	+	0.0139093i
$507$		−	1.52097e18i		−	3.97713i
$508$	−1.57360e17	+	6.52703e17i	−0.406239	+	1.68501i
$509$			3.12464e17i			0.796407i	0.917297	+	0.398203i	$0.130366\pi$
$509$			3.12464e17i			0.796407i	−0.917297	+	0.398203i	$0.869634\pi$
$510$	3.87093e17	+	4.91509e17i	0.974114	+	1.23687i
$511$	−8.41616e16			−0.209112
$512$	1.12331e17	−	3.91836e17i	0.275579	−	0.961278i
$513$	−1.65080e17			−0.399882
$514$	−3.00671e17	−	3.81775e17i	−0.719170	−	0.913161i
$515$		−	4.48820e17i		−	1.06005i
$516$	6.42745e16	−	2.66599e17i	0.149905	−	0.621779i
$517$		−	1.79482e17i		−	0.413363i
$518$	−1.64503e17	+	1.29557e17i	−0.374138	+	0.294657i
$519$	−2.45267e17			−0.550872
$520$	−4.72818e17	+	2.17150e17i	−1.04875	+	0.481658i
$521$	6.34137e17			1.38911			0.694557	−	0.719438i	$-0.255601\pi$
$521$	6.34137e17			1.38911			0.694557	+	0.719438i	$0.255601\pi$
$522$	−4.13533e17	+	3.25683e17i	−0.894647	+	0.704590i
$523$			5.35235e17i			1.14363i	0.820384	+	0.571813i	$0.193760\pi$
$523$			5.35235e17i			1.14363i	−0.820384	+	0.571813i	$0.806240\pi$
$524$	−7.01215e17	−	1.69056e17i	−1.47978	−	0.356761i
$525$		−	2.86693e17i		−	0.597560i
$526$	−2.83759e17	−	3.60301e17i	−0.584175	−	0.741751i
$527$	7.69745e17			1.56523
$528$	3.60989e17	+	1.84803e17i	0.725058	+	0.371184i
$529$	−5.02770e17			−0.997488
$530$	−2.10220e17	−	2.66926e17i	−0.411985	−	0.523115i
$531$			4.67680e17i			0.905387i
$532$	−4.87000e16	−	1.17411e16i	−0.0931330	−	0.0224535i
$533$			7.31887e17i			1.38267i
$534$	−1.67063e16	+	1.31573e16i	−0.0311791	+	0.0245554i
$535$	−1.69698e17			−0.312879
$536$	1.16417e17	+	2.53483e17i	0.212053	+	0.461719i
$537$	−1.36141e18			−2.44995
$538$	−2.25665e17	+	1.77725e17i	−0.401216	+	0.315983i
$539$		−	1.73854e17i		−	0.305392i
$540$	2.05747e17	−	8.53402e17i	0.357087	−	1.48113i
$541$		−	1.04651e18i		−	1.79457i	−0.441448	−	0.897287i	$-0.645535\pi$
$541$		−	1.04651e18i		−	1.79457i	0.441448	−	0.897287i	$-0.354465\pi$
$542$	4.20544e17	+	5.33982e17i	0.712551	+	0.904756i
$543$	8.95153e17			1.49864
$544$	−1.56317e17	−	7.95795e17i	−0.258591	−	1.31646i
$545$	−3.20413e17			−0.523761
$546$	7.01843e17	+	8.91159e17i	1.13367	+	1.43947i
$547$		−	4.15648e17i		−	0.663450i	−0.943376	−	0.331725i	$-0.892369\pi$
$547$		−	4.15648e17i		−	0.663450i	0.943376	−	0.331725i	$-0.107631\pi$
$548$	2.53981e17	−	1.05347e18i	0.400616	−	1.66168i
$549$			1.55424e18i			2.42268i
$550$	1.33233e17	−	1.04929e17i	0.205237	−	0.161637i
$551$	5.51993e16			0.0840326
$552$	−2.52521e16	−	5.49833e16i	−0.0379921	−	0.0827232i
$553$	6.40991e16			0.0953100
$554$	3.17132e17	−	2.49761e17i	0.466044	−	0.367038i
$555$			6.81168e17i			0.989350i
$556$	−1.24551e17	−	3.00279e16i	−0.178797	−	0.0431062i
$557$			3.27692e16i			0.0464950i	0.999730	+	0.0232475i	$0.00740058\pi$
$557$			3.27692e16i			0.0464950i	−0.999730	+	0.0232475i	$0.992599\pi$
$558$	−1.18296e18	−	1.50206e18i	−1.65901	−	2.10651i
$559$	4.53759e17			0.628997
$560$	1.21394e17	−	2.37127e17i	0.166332	−	0.324907i
$561$	8.06871e17			1.09281
$562$	7.39090e17	+	9.38453e17i	0.989489	+	1.25640i
$563$			9.84502e17i			1.30290i	0.758691	+	0.651451i	$0.225839\pi$
$563$			9.84502e17i			1.30290i	−0.758691	+	0.651451i	$0.774161\pi$
$564$	1.24380e18	+	2.99869e17i	1.62719	+	0.392299i
$565$		−	5.72842e16i		−	0.0740832i
$566$	3.85540e17	−	3.03636e17i	0.492904	−	0.388192i
$567$	−8.86680e17			−1.12067
$568$	−8.82312e17	+	4.05218e17i	−1.10245	+	0.506319i
$569$	6.47270e16			0.0799569			0.0399784	−	0.999201i	$-0.487271\pi$
$569$	6.47270e16			0.0799569			0.0399784	+	0.999201i	$0.487271\pi$
$570$	−1.28025e17	+	1.00827e17i	−0.156353	+	0.123138i
$571$		−	5.72438e17i		−	0.691185i	−0.938385	−	0.345592i	$-0.887678\pi$
$571$		−	5.72438e17i		−	0.691185i	0.938385	−	0.345592i	$-0.112322\pi$
$572$	−1.57270e17	+	6.52328e17i	−0.187746	+	0.778738i
$573$			2.42424e17i			0.286135i
$574$	−2.31851e17	−	2.94391e17i	−0.270572	−	0.343556i
$575$	−2.53022e16			−0.0291956
$576$	−1.31266e18	+	1.52803e18i	−1.49763	+	1.74335i
$577$	4.00636e17			0.451968			0.225984	−	0.974131i	$-0.427440\pi$
$577$	4.00636e17			0.451968			0.225984	+	0.974131i	$0.427440\pi$
$578$	−4.43693e17	−	5.63376e17i	−0.494939	−	0.628445i
$579$		−	8.80609e17i		−	0.971343i
$580$	−6.87974e16	+	2.85359e17i	−0.0750395	+	0.311251i
$581$		−	1.53465e17i		−	0.165525i
$582$	−1.00405e18	+	7.90753e17i	−1.07092	+	0.843416i
$583$	−4.38190e17			−0.462187
$584$	3.22509e17	−	1.48118e17i	0.336402	−	0.154499i
$585$	2.57129e18			2.65239
$586$	9.57828e17	−	7.54348e17i	0.977131	−	0.769551i
$587$			4.52980e17i			0.457016i	0.973542	+	0.228508i	$0.0733848\pi$
$587$			4.52980e17i			0.457016i	−0.973542	+	0.228508i	$0.926615\pi$
$588$	1.20480e18	+	2.90466e17i	1.20216	+	0.289829i
$589$			2.00498e17i			0.197861i
$590$	1.61362e17	+	2.04888e17i	0.157493	+	0.199976i
$591$	−1.00863e18			−0.973669
$592$	4.02371e17	−	7.85978e17i	0.384181	−	0.750445i
$593$	−6.40224e17			−0.604611			−0.302306	−	0.953211i	$-0.597756\pi$
$593$	−6.40224e17			−0.604611			−0.302306	+	0.953211i	$0.597756\pi$
$594$	−7.00481e17	−	8.89430e17i	−0.654311	−	0.830807i
$595$		−	5.30020e17i		−	0.489702i
$596$	−7.05606e17	−	1.70115e17i	−0.644854	−	0.155468i
$597$		−	2.64452e18i		−	2.39064i
$598$	7.86495e16	−	6.19414e16i	0.0703297	−	0.0553889i
$599$	1.47546e17			0.130512			0.0652562	−	0.997869i	$-0.479214\pi$
$599$	1.47546e17			0.130512			0.0652562	+	0.997869i	$0.479214\pi$
$600$	5.04559e17	+	1.09861e18i	0.441498	+	0.961307i
$601$	−2.18719e18			−1.89323			−0.946613	−	0.322374i	$-0.895519\pi$
$601$	−2.18719e18			−1.89323			−0.946613	+	0.322374i	$0.895519\pi$
$602$	−1.82518e17	+	1.43744e17i	−0.156289	+	0.123087i
$603$		−	1.37850e18i		−	1.16773i
$604$	1.65284e17	−	6.85570e17i	0.138513	−	0.574529i
$605$		−	6.22604e17i		−	0.516181i
$606$	2.06661e17	+	2.62406e17i	0.169506	+	0.215230i
$607$	−9.26716e17			−0.752004			−0.376002	−	0.926619i	$-0.622701\pi$
$607$	−9.26716e17			−0.752004			−0.376002	+	0.926619i	$0.622701\pi$
$608$	2.07283e17	−	4.07163e16i	0.166414	−	0.0326885i
$609$	6.39963e17			0.508326
$610$	5.36252e17	+	6.80902e17i	0.421430	+	0.535107i
$611$			2.11698e18i			1.64607i
$612$	−9.39359e17	+	3.89630e18i	−0.722682	+	2.99756i
$613$		−	4.80242e17i		−	0.365567i	−0.983153	−	0.182783i	$-0.941489\pi$
$613$		−	4.80242e17i		−	0.365567i	0.983153	−	0.182783i	$-0.0585107\pi$
$614$	−1.21086e17	+	9.53630e16i	−0.0912013	+	0.0718266i
$615$	−1.21900e18			−0.908481
$616$	−1.43388e17	−	3.12210e17i	−0.105740	−	0.230236i
$617$	−1.37389e18			−1.00253			−0.501267	−	0.865293i	$-0.667132\pi$
$617$	−1.37389e18			−1.00253			−0.501267	+	0.865293i	$0.667132\pi$
$618$	3.24162e18	−	2.55297e18i	2.34065	−	1.84341i
$619$			2.52941e18i			1.80730i	0.428270	+	0.903651i	$0.359123\pi$
$619$			2.52941e18i			1.80730i	−0.428270	+	0.903651i	$0.640877\pi$
$620$	−1.03650e18	−	2.49889e17i	−0.732862	−	0.176686i
$621$			1.68911e17i			0.118185i
$622$	9.32718e17	+	1.18431e18i	0.645822	+	0.820027i
$623$	1.80153e16			0.0123444
$624$	−4.25785e18	−	2.17975e18i	−2.88729	−	1.47811i
$625$	−1.16605e17			−0.0782520
$626$	7.74427e17	+	9.83323e17i	0.514337	+	0.653075i
$627$			2.10168e17i			0.138143i
$628$	1.99836e18	+	4.81785e17i	1.29998	+	0.313412i
$629$		−	1.75679e18i		−	1.13108i
$630$	−1.03426e18	+	8.14547e17i	−0.659050	+	0.519042i
$631$	2.14602e18			1.35345			0.676727	−	0.736234i	$-0.263398\pi$
$631$	2.14602e18			1.35345			0.676727	+	0.736234i	$0.263398\pi$
$632$	−2.45629e17	+	1.12810e17i	−0.153327	+	0.0704182i
$633$	3.70447e18			2.28877
$634$	−7.96392e17	+	6.27207e17i	−0.487020	+	0.383558i
$635$		−	1.85030e18i		−	1.11999i
$636$	7.32106e17	−	3.03665e18i	0.438634	−	1.81938i
$637$			2.05060e18i			1.21612i
$638$	2.34226e17	+	2.97407e17i	0.137499	+	0.174589i
$639$	4.79821e18			2.78820
$640$	−4.78584e16	+	1.12232e18i	−0.0275289	+	0.645577i
$641$	−9.09162e17			−0.517683			−0.258842	−	0.965920i	$-0.583341\pi$
$641$	−9.09162e17			−0.517683			−0.258842	+	0.965920i	$0.583341\pi$
$642$	−9.65272e17	−	1.22565e18i	−0.544092	−	0.690856i
$643$		−	9.02957e17i		−	0.503844i	−0.967748	−	0.251922i	$-0.918937\pi$
$643$		−	9.02957e17i		−	0.503844i	0.967748	−	0.251922i	$-0.0810626\pi$
$644$	−1.20135e16	+	4.98301e16i	−0.00663610	+	0.0275254i
$645$			7.55762e17i			0.413282i
$646$	3.30188e17	−	2.60043e17i	0.178751	−	0.140778i
$647$	−1.80761e18			−0.968781			−0.484391	−	0.874852i	$-0.660959\pi$
$647$	−1.80761e18			−0.968781			−0.484391	+	0.874852i	$0.660959\pi$
$648$	3.39778e18	−	1.56049e18i	1.80284	−	0.827987i
$649$	3.36348e17			0.176684
$650$	−1.57148e18	+	1.23764e18i	−0.817284	+	0.643662i
$651$			2.32451e18i			1.19689i
$652$	−8.82601e17	−	2.12787e17i	−0.449941	−	0.108476i
$653$			2.17100e18i			1.09578i	0.836550	+	0.547890i	$0.184569\pi$
$653$			2.17100e18i			1.09578i	−0.836550	+	0.547890i	$0.815431\pi$
$654$	−1.82257e18	−	2.31420e18i	−0.910813	−	1.15650i
$655$	1.98782e18			0.983577
$656$	1.40657e18	+	7.20073e17i	0.689105	+	0.352778i
$657$	−1.75388e18			−0.850794
$658$	−6.70629e17	−	8.51526e17i	−0.322117	−	0.409006i
$659$		−	9.62092e16i		−	0.0457574i	−0.999738	−	0.0228787i	$-0.992717\pi$
$659$		−	9.62092e16i		−	0.0457574i	0.999738	−	0.0228787i	$-0.00728315\pi$
$660$	−1.08649e18	−	2.61942e17i	−0.511670	−	0.123359i
$661$			1.03573e18i			0.482990i	0.970402	+	0.241495i	$0.0776377\pi$
$661$			1.03573e18i			0.482990i	−0.970402	+	0.241495i	$0.922362\pi$
$662$	2.93174e18	−	2.30892e18i	1.35378	−	1.06619i
$663$	−9.51702e18			−4.35174
$664$	2.70087e17	+	5.88080e17i	0.122296	+	0.266283i
$665$	1.38056e17			0.0619034
$666$	−3.42815e18	+	2.69988e18i	−1.52222	+	1.19884i
$667$		−	5.64801e16i		−	0.0248358i
$668$	−4.24136e17	+	1.75924e18i	−0.184696	+	0.766088i
$669$			4.03850e18i			1.74161i
$670$	−4.75619e17	−	6.03913e17i	−0.203129	−	0.257922i
$671$	1.11778e18			0.472782
$672$	2.40317e18	−	4.72052e17i	1.00666	−	0.197738i
$673$	1.08936e18			0.451934			0.225967	−	0.974135i	$-0.427446\pi$
$673$	1.08936e18			0.451934			0.225967	+	0.974135i	$0.427446\pi$
$674$	3.43137e17	+	4.35695e17i	0.140987	+	0.179017i
$675$		−	3.37498e18i		−	1.37340i
$676$	1.27347e18	−	5.28214e18i	0.513259	−	2.12891i
$677$		−	4.37578e18i		−	1.74674i	−0.487055	−	0.873371i	$-0.661929\pi$
$677$		−	4.37578e18i		−	1.74674i	0.487055	−	0.873371i	$-0.338071\pi$
$678$	4.13737e17	−	3.25843e17i	0.163580	−	0.128830i
$679$	1.08272e18			0.423998
$680$	9.32797e17	+	2.03105e18i	0.361809	+	0.787794i
$681$	−8.04164e18			−3.08950
$682$	−1.08026e18	+	8.50768e17i	−0.411082	+	0.323752i
$683$		−	3.73721e18i		−	1.40868i	−0.709862	−	0.704341i	$-0.751243\pi$
$683$		−	3.73721e18i		−	1.40868i	0.709862	−	0.704341i	$-0.248757\pi$
$684$	−1.01488e18	−	2.44678e17i	−0.378922	−	0.0913544i
$685$			2.98640e18i			1.10448i
$686$	−1.60363e18	−	2.03619e18i	−0.587485	−	0.745954i
$687$	6.79424e18			2.46560
$688$	4.46434e17	−	8.72049e17i	0.160484	−	0.313485i
$689$	5.16845e18			1.84050
$690$	1.03167e17	+	1.30995e17i	0.0363933	+	0.0462101i
$691$		−	3.04942e18i		−	1.06564i	−0.846229	−	0.532819i	$-0.821132\pi$
$691$		−	3.04942e18i		−	1.06564i	0.846229	−	0.532819i	$-0.178868\pi$
$692$	−8.51779e17	−	2.05356e17i	−0.294875	−	0.0710914i
$693$			1.69787e18i			0.582289i
$694$	−3.97687e18	+	3.13203e18i	−1.35116	+	1.06412i
$695$	3.53079e17			0.118842
$696$	−2.45235e18	+	1.12629e18i	−0.817754	+	0.375568i
$697$	3.14392e18			1.03862
$698$	−2.11660e18	+	1.66696e18i	−0.692755	+	0.545587i
$699$			4.26258e18i			1.38220i
$700$	2.40041e17	−	9.95647e17i	0.0771166	−	0.319866i
$701$		−	3.76321e18i		−	1.19782i	−0.800817	−	0.598909i	$-0.795601\pi$
$701$		−	3.76321e18i		−	1.19782i	0.800817	−	0.598909i	$-0.204399\pi$
$702$	8.26216e18	+	1.04908e19i	2.60557	+	3.30840i
$703$	4.57597e17			0.142980
$704$	1.09893e18	+	9.44044e17i	0.340212	+	0.292260i
$705$	−3.52596e18			−1.08155
$706$	2.59080e18	+	3.28964e18i	0.787413	+	0.999811i
$707$		−	2.82967e17i		−	0.0852136i
$708$	−5.61953e17	+	2.33088e18i	−0.167681	+	0.695511i
$709$		−	9.76223e17i		−	0.288635i	−0.989531	−	0.144317i	$-0.953901\pi$
$709$		−	9.76223e17i		−	0.288635i	0.989531	−	0.144317i	$-0.0460986\pi$
$710$	2.10207e18	−	1.65551e18i	0.615840	−	0.485012i
$711$	1.33579e18			0.387779
$712$	−6.90351e16	+	3.17057e16i	−0.0198587	+	0.00912046i
$713$	2.05150e17			0.0584776
$714$	3.82809e18	−	3.01486e18i	1.08129	−	0.851585i
$715$		−	1.84923e18i		−	0.517609i
$716$	−4.72801e18	−	1.13988e18i	−1.31143	−	0.316172i
$717$		−	8.53030e18i		−	2.34471i
$718$	−3.17736e18	−	4.03442e18i	−0.865480	−	1.09894i
$719$	−3.07436e18			−0.829883			−0.414942	−	0.909848i	$-0.636198\pi$
$719$	−3.07436e18			−0.829883			−0.414942	+	0.909848i	$0.636198\pi$
$720$	2.52978e18	−	4.94159e18i	0.676740	−	1.32192i
$721$	−3.49561e18			−0.926710
$722$	−2.28723e18	−	2.90420e18i	−0.600923	−	0.763017i
$723$			8.79290e18i			2.28946i
$724$	3.10875e18	+	7.49489e17i	0.802204	+	0.193404i
$725$			1.12852e18i			0.288611i
$726$	4.49678e18	−	3.54149e18i	1.13976	−	0.897631i
$727$	1.90198e18			0.477786			0.238893	−	0.971046i	$-0.423216\pi$
$727$	1.90198e18			0.477786			0.238893	+	0.971046i	$0.423216\pi$
$728$	1.69126e18	+	3.68251e18i	0.421073	+	0.916833i
$729$	−1.12408e18			−0.277377
$730$	−7.68364e17	+	6.05134e17i	−0.187918	+	0.147997i
$731$		−	1.94918e18i		−	0.472486i
$732$	−1.86753e18	+	7.74620e18i	−0.448690	+	1.86109i
$733$			6.34136e18i			1.51010i	0.655666	+	0.755051i	$0.272388\pi$
$733$			6.34136e18i			1.51010i	−0.655666	+	0.755051i	$0.727612\pi$
$734$	4.82133e18	+	6.12185e18i	1.13800	+	1.44497i
$735$	−3.41540e18			−0.799049
$736$	−4.16611e16	−	2.12093e17i	−0.00966106	−	0.0491836i
$737$	−9.91396e17			−0.227881
$738$	−4.83164e18	−	6.13494e18i	−1.10085	−	1.39780i
$739$		−	7.23191e17i		−	0.163329i	−0.996660	−	0.0816646i	$-0.973976\pi$
$739$		−	7.23191e17i		−	0.163329i	0.996660	−	0.0816646i	$-0.0260236\pi$
$740$	−5.70325e17	+	2.36561e18i	−0.127678	+	0.529586i
$741$		−	2.47893e18i		−	0.550105i
$742$	−2.07893e18	+	1.63729e18i	−0.457315	+	0.360164i
$743$	−4.90951e18			−1.07056			−0.535279	−	0.844675i	$-0.679794\pi$
$743$	−4.90951e18			−1.07056			−0.535279	+	0.844675i	$0.679794\pi$
$744$	−4.09096e18	−	8.90756e18i	−0.884303	−	1.92546i
$745$	2.00027e18			0.428620
$746$	−3.64458e18	+	2.87033e18i	−0.774185	+	0.609718i
$747$		−	3.19811e18i		−	0.673457i
$748$	2.80216e18	+	6.75573e17i	0.584968	+	0.141030i
$749$			1.32168e18i			0.273523i
$750$	−5.60035e18	−	7.11100e18i	−1.14899	−	1.45892i
$751$	−1.58181e18			−0.321733			−0.160867	−	0.986976i	$-0.551429\pi$
$751$	−1.58181e18			−0.321733			−0.160867	+	0.986976i	$0.551429\pi$
$752$	4.06849e18	+	2.08281e18i	0.820384	+	0.419985i
$753$	1.32041e19			2.63961
$754$	−2.76269e18	−	3.50790e18i	−0.547543	−	0.695239i
$755$			1.94347e18i			0.381876i
$756$	−6.64667e18	−	1.60245e18i	−1.29483	−	0.312171i
$757$			6.28404e18i			1.21371i	0.794812	+	0.606856i	$0.207570\pi$
$757$			6.28404e18i			1.21371i	−0.794812	+	0.606856i	$0.792430\pi$
$758$	9.49903e17	−	7.48107e17i	0.181899	−	0.143256i
$759$	2.15045e17			0.0408279
$760$	−5.29033e17	+	2.42968e17i	−0.0995852	+	0.0457363i
$761$	9.49858e18			1.77280			0.886398	−	0.462925i	$-0.153200\pi$
$761$	9.49858e18			1.77280			0.886398	+	0.462925i	$0.153200\pi$
$762$	1.33638e19	−	1.05248e19i	2.47300	−	1.94764i
$763$			2.49552e18i			0.457880i
$764$	−2.02976e17	+	8.41908e17i	−0.0369264	+	0.153164i
$765$		−	1.10453e19i		−	1.99241i
$766$	−3.73081e18	−	4.73717e18i	−0.667292	−	0.847289i
$767$	−3.96722e18			−0.703584
$768$	−8.37824e18	+	6.03832e18i	−1.47335	+	1.06186i
$769$	−7.21806e18			−1.25863			−0.629317	−	0.777149i	$-0.716665\pi$
$769$	−7.21806e18			−1.25863			−0.629317	+	0.777149i	$0.716665\pi$
$770$	5.85810e17	+	7.43828e17i	0.101290	+	0.128612i
$771$			1.23122e19i			2.11098i
$772$	7.37312e17	−	3.05824e18i	0.125354	−	0.519947i
$773$			3.55658e18i			0.599606i	0.954001	+	0.299803i	$0.0969209\pi$
$773$			3.55658e18i			0.599606i	−0.954001	+	0.299803i	$0.903079\pi$
$774$	−3.80357e18	+	2.99554e18i	−0.635879	+	0.500794i
$775$	−4.09907e18			−0.679554
$776$	−4.14902e18	+	1.90551e18i	−0.682094	+	0.313264i
$777$	5.30524e18			0.864905
$778$	−1.78145e18	+	1.40300e18i	−0.288008	+	0.226824i
$779$			8.18905e17i			0.131293i
$780$	1.28151e19	+	3.08960e18i	2.03755	+	0.491233i
$781$		−	3.45080e18i		−	0.544112i
$782$	−2.66077e17	−	3.37849e17i	−0.0416067	−	0.0528298i
$783$	7.53370e18			1.16831
$784$	3.94091e18	+	2.01750e18i	0.606098	+	0.310284i
$785$	−5.66499e18			−0.864065
$786$	1.13071e19	+	1.43571e19i	1.71043	+	2.17180i
$787$		−	1.06955e19i		−	1.60459i	−0.596927	−	0.802295i	$-0.703612\pi$
$787$		−	1.06955e19i		−	1.60459i	0.596927	−	0.802295i	$-0.296388\pi$
$788$	−3.50283e18	−	8.44497e17i	−0.521192	−	0.125654i
$789$			1.16197e19i			1.71473i
$790$	5.85200e17	−	4.60881e17i	0.0856502	−	0.0674548i
$791$	−4.46155e17			−0.0647647
$792$	−2.98813e18	−	6.50628e18i	−0.430215	−	0.936740i
$793$	−1.31842e19			−1.88269
$794$	2.43607e17	−	1.91856e17i	0.0345030	−	0.0271733i
$795$			8.60835e18i			1.20930i
$796$	2.21419e18	−	9.18408e18i	0.308518	−	1.27968i
$797$		−	5.89304e18i		−	0.814443i	−0.913329	−	0.407221i	$-0.866498\pi$
$797$		−	5.89304e18i		−	0.814443i	0.913329	−	0.407221i	$-0.133502\pi$
$798$	7.85288e17	+	9.97113e17i	0.107649	+	0.136687i
$799$	9.09377e18			1.23649
$800$	8.32424e17	+	4.23779e18i	0.112269	+	0.571551i
$801$	3.75429e17			0.0502246
$802$	3.53427e18	+	4.48761e18i	0.468993	+	0.595500i
$803$			1.26136e18i			0.166031i
$804$	1.65637e18	−	6.87034e18i	0.216269	−	0.897044i
$805$		−	1.41259e17i		−	0.0182955i
$806$	1.27416e19	−	1.00348e19i	1.63699	−	1.28923i
$807$	7.27768e18			0.927503
$808$	4.98000e17	+	1.08433e18i	0.0629587	+	0.137085i
$809$	−4.31840e18			−0.541574			−0.270787	−	0.962639i	$-0.587284\pi$
$809$	−4.31840e18			−0.541574			−0.270787	+	0.962639i	$0.587284\pi$
$810$	−8.09505e18	+	6.37535e18i	−1.00709	+	0.793143i
$811$		−	6.94897e18i		−	0.857600i	−0.903400	−	0.428800i	$-0.858937\pi$
$811$		−	6.94897e18i		−	0.857600i	0.903400	−	0.428800i	$-0.141063\pi$
$812$	2.22251e18	+	5.35825e17i	0.272100	+	0.0656007i
$813$		−	1.72209e19i		−	2.09155i
$814$	1.94171e18	+	2.46548e18i	0.233952	+	0.297059i
$815$	2.50202e18			0.299065
$816$	−9.36339e18	+	1.82901e19i	−1.11032	+	2.16886i
$817$	5.07708e17			0.0597270
$818$	−2.62213e18	−	3.32943e18i	−0.306026	−	0.388574i
$819$		−	2.00263e19i		−	2.31876i
$820$	−4.23343e18	−	1.02064e18i	−0.486298	−	0.117242i
$821$		−	1.02659e19i		−	1.16994i	−0.811053	−	0.584972i	$-0.801105\pi$
$821$		−	1.02659e19i		−	1.16994i	0.811053	−	0.584972i	$-0.198895\pi$
$822$	−2.15694e19	+	1.69872e19i	−2.43877	+	1.92068i
$823$	−6.63515e18			−0.744307			−0.372153	−	0.928171i	$-0.621380\pi$
$823$	−6.63515e18			−0.744307			−0.372153	+	0.928171i	$0.621380\pi$
$824$	1.33953e19	−	6.15202e18i	1.49082	−	0.684685i
$825$	−4.29678e18			−0.474452
$826$	1.59576e18	−	1.25676e18i	0.174822	−	0.137683i
$827$			1.36543e19i			1.48417i	0.670306	+	0.742085i	$0.266163\pi$
$827$			1.36543e19i			1.48417i	−0.670306	+	0.742085i	$0.733837\pi$
$828$	−2.50355e17	+	1.03843e18i	−0.0269997	+	0.111990i
$829$			9.78629e18i			1.04716i	0.851976	+	0.523581i	$0.175404\pi$
$829$			9.78629e18i			1.04716i	−0.851976	+	0.523581i	$0.824596\pi$
$830$	−1.10343e18	−	1.40108e18i	−0.117149	−	0.148749i
$831$	−1.02275e19			−1.07737
$832$	−1.29619e19	−	1.11350e19i	−1.35478	−	1.16382i
$833$	8.80862e18			0.913514
$834$	2.00838e18	+	2.55012e18i	0.206665	+	0.262411i
$835$		−	4.98714e18i		−	0.509201i
$836$	−1.75968e17	+	7.29886e17i	−0.0178276	+	0.0739459i
$837$			2.73643e19i			2.75086i
$838$	−1.26016e19	+	9.92450e18i	−1.25701	+	0.989971i
$839$	1.81737e18			0.179883			0.0899414	−	0.995947i	$-0.471332\pi$
$839$	1.81737e18			0.179883			0.0899414	+	0.995947i	$0.471332\pi$
$840$	−6.13344e18	+	2.81690e18i	−0.602405	+	0.276666i
$841$	7.74152e18			0.754488
$842$	−3.28516e18	+	2.58727e18i	−0.317708	+	0.250215i
$843$		−	3.02651e19i		−	2.90444i
$844$	1.28651e19	+	3.10166e18i	1.22515	+	0.295371i
$845$			1.49739e19i			1.41504i
$846$	−1.39755e19	−	1.77453e19i	−1.31057	−	1.66409i
$847$	−4.84911e18			−0.451253
$848$	5.08501e18	−	9.93290e18i	0.469590	−	0.917282i
$849$	−1.24337e19			−1.13946
$850$	5.31644e18	+	6.75051e18i	0.483502	+	0.613923i
$851$		−	4.68215e17i		−	0.0422575i
$852$	2.39139e19	+	5.76542e18i	2.14187	+	0.516385i
$853$		−	1.08807e19i		−	0.967141i	−0.875305	−	0.483570i	$-0.839340\pi$
$853$		−	1.08807e19i		−	0.967141i	0.875305	−	0.483570i	$-0.160660\pi$
$854$	5.30317e18	−	4.17657e18i	0.467799	−	0.368420i
$855$	2.87700e18			0.251861
$856$	−2.32606e18	−	5.06471e18i	−0.202088	−	0.440022i
$857$	−1.14054e19			−0.983410			−0.491705	−	0.870762i	$-0.663626\pi$
$857$	−1.14054e19			−0.983410			−0.491705	+	0.870762i	$0.663626\pi$
$858$	1.33561e19	−	1.05188e19i	1.14291	−	0.900115i
$859$			4.02770e18i			0.342059i	0.985266	+	0.171030i	$0.0547094\pi$
$859$			4.02770e18i			0.342059i	−0.985266	+	0.171030i	$0.945291\pi$
$860$	−6.32780e17	+	2.62466e18i	−0.0533351	+	0.221225i
$861$			9.49412e18i			0.794208i
$862$	8.29333e18	+	1.05304e19i	0.688544	+	0.874273i
$863$	1.23712e19			1.01940			0.509698	−	0.860353i	$-0.329757\pi$
$863$	1.23712e19			1.01940			0.509698	+	0.860353i	$0.329757\pi$
$864$	2.82904e19	−	5.55704e18i	2.31366	−	0.454469i
$865$	2.41464e18			0.195996
$866$	−1.03251e19	−	1.31102e19i	−0.831815	−	1.05619i
$867$			1.81689e19i			1.45279i
$868$	−1.94625e18	+	8.07270e18i	−0.154462	+	0.640679i
$869$		−	9.60677e17i		−	0.0756744i
$870$	5.84262e18	−	4.60142e18i	0.456807	−	0.359763i
$871$	1.16935e19			0.907457
$872$	−4.39193e18	−	9.56289e18i	−0.338297	−	0.736600i
$873$	2.25633e19			1.72508
$874$	8.80006e16	−	6.93059e16i	0.00667823	−	0.00525951i
$875$			7.66817e18i			0.577616i
$876$	−8.74120e18	−	2.10742e18i	−0.653573	−	0.157570i
$877$			1.56172e18i			0.115906i	0.998319	+	0.0579529i	$0.0184573\pi$
$877$			1.56172e18i			0.115906i	−0.998319	+	0.0579529i	$0.981543\pi$
$878$	8.18068e18	+	1.03874e19i	0.602664	+	0.765227i
$879$	−3.08899e19			−2.25886
$880$	−3.55392e18	−	1.81938e18i	−0.257971	−	0.132065i
$881$	7.20663e18			0.519265			0.259632	−	0.965707i	$-0.416399\pi$
$881$	7.20663e18			0.519265			0.259632	+	0.965707i	$0.416399\pi$
$882$	−1.35373e19	−	1.71889e19i	−0.968246	−	1.22942i
$883$			2.00295e19i			1.42209i	0.703147	+	0.711044i	$0.251777\pi$
$883$			2.00295e19i			1.42209i	−0.703147	+	0.711044i	$0.748223\pi$
$884$	−3.30514e19	−	7.96836e18i	−2.32943	−	0.561603i
$885$		−	6.60763e18i		−	0.462290i
$886$	−2.64531e18	+	2.08334e18i	−0.183720	+	0.144691i
$887$	2.69642e19			1.85902			0.929508	−	0.368801i	$-0.120232\pi$
$887$	2.69642e19			1.85902			0.929508	+	0.368801i	$0.120232\pi$
$888$	−2.03298e19	+	9.33683e18i	−1.39139	+	0.639021i
$889$	−1.44109e19			−0.979108
$890$	1.64473e17	−	1.29533e17i	0.0110933	−	0.00873664i
$891$			1.32890e19i			0.889790i
$892$	−3.38133e18	+	1.40252e19i	−0.224759	+	0.932259i
$893$			2.36868e18i			0.156305i
$894$	1.13779e19	+	1.44470e19i	0.745364	+	0.946420i
$895$	1.34031e19			0.871675
$896$	8.74114e18	+	3.72742e17i	0.564373	+	0.0240662i
$897$	−2.53645e18			−0.162583
$898$	6.61728e18	+	8.40224e18i	0.421098	+	0.534686i
$899$		−	9.15004e18i		−	0.578076i
$900$	5.00231e18	−	2.07487e19i	0.313757	−	1.30141i
$901$		−	2.22017e19i		−	1.38253i
$902$	−4.41215e18	+	3.47484e18i	−0.272777	+	0.214829i
$903$	5.88621e18			0.361298
$904$	1.70967e18	−	7.85199e17i	0.104188	−	0.0478504i
$905$	−8.81274e18			−0.533206
$906$	−1.40368e19	+	1.10548e19i	−0.843207	+	0.664077i
$907$		−	7.37547e18i		−	0.439888i	−0.975512	−	0.219944i	$-0.929412\pi$
$907$		−	7.37547e18i		−	0.439888i	0.975512	−	0.219944i	$-0.0705875\pi$
$908$	−2.79275e19	−	6.73306e18i	−1.65377	−	0.398708i
$909$		−	5.89685e18i		−	0.346701i
$910$	−6.90961e18	−	8.77343e18i	−0.403353	−	0.512154i
$911$	−2.93994e19			−1.70400			−0.851999	−	0.523544i	$-0.824610\pi$
$911$	−2.93994e19			−1.70400			−0.851999	+	0.523544i	$0.824610\pi$
$912$	−4.76409e18	−	2.43891e18i	−0.274166	−	0.140355i
$913$	−2.30004e18			−0.131424
$914$	−6.92035e18	−	8.78706e18i	−0.392625	−	0.498532i
$915$		−	2.19591e19i		−	1.23702i
$916$	2.35955e19	+	5.68865e18i	1.31980	+	0.318191i
$917$		−	1.54820e19i		−	0.859858i
$918$	4.50646e19	−	3.54911e19i	2.48518	−	1.95723i
$919$	1.69470e19			0.927986			0.463993	−	0.885839i	$-0.346416\pi$
$919$	1.69470e19			0.927986			0.463993	+	0.885839i	$0.346416\pi$
$920$	2.48606e17	+	5.41309e17i	0.0135173	+	0.0294323i
$921$	3.90504e18			0.210832
$922$	1.50925e19	−	1.18863e19i	0.809116	−	0.637229i
$923$			4.07021e19i			2.16673i
$924$	−2.04012e18	+	8.46206e18i	−0.107842	+	0.447310i
$925$			9.35534e18i			0.491064i
$926$	7.51718e18	+	9.54489e18i	0.391817	+	0.497507i
$927$	−7.28464e19			−3.77042
$928$	−9.45970e18	+	1.85816e18i	−0.486201	+	0.0955037i
$929$	7.12343e17			0.0363569			0.0181785	−	0.999835i	$-0.494213\pi$
$929$	7.12343e17			0.0363569			0.0181785	+	0.999835i	$0.494213\pi$
$930$	1.67135e19	+	2.12219e19i	0.847089	+	1.07558i
$931$			2.29441e18i			0.115477i
$932$	−3.56895e18	+	1.48034e19i	−0.178376	+	0.739874i
$933$		−	3.81940e19i		−	1.89568i
$934$	−5.96523e17	+	4.69799e17i	−0.0294017	+	0.0231557i
$935$	−7.94361e18			−0.388815
$936$	3.52449e19	+	7.67414e19i	1.71318	+	3.73024i
$937$	2.82178e19			1.36212			0.681060	−	0.732227i	$-0.261519\pi$
$937$	2.82178e19			1.36212			0.681060	+	0.732227i	$0.261519\pi$
$938$	−4.70354e18	+	3.70433e18i	−0.225479	+	0.177579i
$939$		−	3.17122e19i		−	1.50973i
$940$	−1.22452e19	−	2.95219e18i	−0.578941	−	0.139577i
$941$			3.73589e19i			1.75413i	0.480372	+	0.877065i	$0.340502\pi$
$941$			3.73589e19i			1.75413i	−0.480372	+	0.877065i	$0.659498\pi$
$942$	−3.22235e19	−	4.09156e19i	−1.50260	−	1.90791i
$943$	8.37907e17			0.0388034
$944$	−3.90318e18	+	7.62433e18i	−0.179515	+	0.350658i
$945$	1.88421e19			0.860643
$946$	2.15435e18	+	2.73547e18i	0.0977291	+	0.124091i
$947$		−	5.74303e18i		−	0.258742i	−0.991596	−	0.129371i	$-0.958704\pi$
$947$		−	5.74303e18i		−	0.258742i	0.991596	−	0.129371i	$-0.0412958\pi$
$948$	6.65746e18	+	1.60505e18i	0.297889	+	0.0718181i
$949$		−	1.48777e19i		−	0.661160i
$950$	−1.75833e18	+	1.38479e18i	−0.0776061	+	0.0611196i
$951$	2.56836e19			1.12586
$952$	1.58187e19	−	7.26503e18i	0.688701	−	0.316299i
$953$	−2.24273e18			−0.0969778			−0.0484889	−	0.998824i	$-0.515441\pi$
$953$	−2.24273e18			−0.0969778			−0.0484889	+	0.998824i	$0.515441\pi$
$954$	−4.33237e19	+	3.41201e19i	−1.86064	+	1.46537i
$955$		−	2.38666e18i		−	0.101805i
$956$	7.14220e18	−	2.96246e19i	0.302591	−	1.25509i
$957$		−	9.59136e18i		−	0.403601i
$958$	1.30212e19	+	1.65335e19i	0.544219	+	0.691018i
$959$	2.32594e19			0.965556
$960$	1.85460e19	−	2.15888e19i	0.764691	−	0.890155i
$961$	8.81770e18			0.361121
$962$	−2.29025e19	−	2.90802e19i	−0.931632	−	1.18293i
$963$			2.75430e19i			1.11286i
$964$	−7.36207e18	+	3.05366e19i	−0.295460	+	1.22552i
$965$			8.66956e18i			0.345597i
$966$	1.02025e18	−	8.03510e17i	0.0403976	−	0.0318156i
$967$	−1.62245e19			−0.638117			−0.319059	−	0.947735i	$-0.603367\pi$
$967$	−1.62245e19			−0.638117			−0.319059	+	0.947735i	$0.603367\pi$
$968$	1.85819e19	−	8.53408e18i	0.725940	−	0.333401i
$969$	−1.06485e19			−0.413224
$970$	9.88486e18	−	7.78494e18i	0.381026	−	0.300081i
$971$		−	4.12888e19i		−	1.58091i	−0.612520	−	0.790455i	$-0.709844\pi$
$971$		−	4.12888e19i		−	1.58091i	0.612520	−	0.790455i	$-0.290156\pi$
$972$	−3.18250e19	−	7.67269e18i	−1.21042	−	0.291821i
$973$		−	2.74993e18i		−	0.103894i
$974$	1.56553e19	+	1.98783e19i	0.587529	+	0.746011i
$975$	5.06804e19			1.88934
$976$	−1.29714e19	+	2.53379e19i	−0.480355	+	0.938310i
$977$	1.12819e19			0.415020			0.207510	−	0.978233i	$-0.433464\pi$
$977$	1.12819e19			0.415020			0.207510	+	0.978233i	$0.433464\pi$
$978$	1.42319e19	+	1.80709e19i	0.520070	+	0.660355i
$979$		−	2.70003e17i		−	0.00980123i
$980$	−1.18612e19	−	2.85962e18i	−0.427720	−	0.103119i
$981$			5.20052e19i			1.86294i
$982$	2.33949e19	−	1.84249e19i	0.832524	−	0.655664i
$983$	−3.06908e19			−1.08495			−0.542476	−	0.840071i	$-0.682513\pi$
$983$	−3.06908e19			−1.08495			−0.542476	+	0.840071i	$0.682513\pi$
$984$	−1.67090e19	−	3.63817e19i	−0.586788	−	1.27766i
$985$	9.92988e18			0.346425
$986$	−1.50686e19	+	1.18675e19i	−0.522245	+	0.411300i
$987$			2.74617e19i			0.945510i
$988$	2.07554e18	−	8.60899e18i	0.0709923	−	0.294464i
$989$		−	5.19489e17i		−	0.0176523i
$990$	1.22079e19	+	1.55009e19i	0.412110	+	0.523273i
$991$	−3.54151e19			−1.18771			−0.593855	−	0.804572i	$-0.702395\pi$
$991$	−3.54151e19			−1.18771			−0.593855	+	0.804572i	$0.702395\pi$
$992$	−6.74929e18	−	3.43600e19i	−0.224870	−	1.14479i
$993$	−9.45486e19			−3.12957
$994$	−1.28938e19	−	1.63718e19i	−0.424005	−	0.538376i
$995$			2.60352e19i			0.850572i
$996$	3.84278e18	−	1.59392e19i	0.124727	−	0.517345i
$997$		−	1.78923e19i		−	0.576962i	−0.957486	−	0.288481i	$-0.906850\pi$
$997$		−	1.78923e19i		−	0.576962i	0.957486	−	0.288481i	$-0.0931502\pi$
$998$	8.57035e18	−	6.74968e18i	0.274568	−	0.216239i
$999$	6.24537e19			1.98785

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.14.b.a.5.1	✓	2
3.2	odd	2		72.14.d.b.37.2		2
4.3	odd	2		32.14.b.a.17.1		2
8.3	odd	2		32.14.b.a.17.2		2
8.5	even	2	inner	8.14.b.a.5.2	yes	2
24.5	odd	2		72.14.d.b.37.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.14.b.a.5.1	✓	2	1.1	even	1	trivial
8.14.b.a.5.2	yes	2	8.5	even	2	inner
32.14.b.a.17.1		2	4.3	odd	2
32.14.b.a.17.2		2	8.3	odd	2
72.14.d.b.37.1		2	24.5	odd	2
72.14.d.b.37.2		2	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	8.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-56.0000 - 71.1056i) q^{2} +2293.15i q^{3} +(-1920.00 + 7963.82i) q^{4} -22576.0i q^{5} +(163056. - 128417. i) q^{6} -175832. q^{7} +(673792. - 309451. i) q^{8} -3.66423e6 q^{9} +O(q^{10})\)	\(q+(-56.0000 - 71.1056i) q^{2} +2293.15i q^{3} +(-1920.00 + 7963.82i) q^{4} -22576.0i q^{5} +(163056. - 128417. i) q^{6} -175832. q^{7} +(673792. - 309451. i) q^{8} -3.66423e6 q^{9} +(-1.60528e6 + 1.26426e6i) q^{10} +2.63526e6i q^{11} +(-1.82623e7 - 4.40286e6i) q^{12} -3.10828e7i q^{13} +(9.84659e6 + 1.25026e7i) q^{14} +5.17703e7 q^{15} +(-5.97361e7 - 3.05811e7i) q^{16} -1.33520e8 q^{17} +(2.05197e8 + 2.60547e8i) q^{18} -3.47784e7i q^{19} +(1.79791e8 + 4.33459e7i) q^{20} -4.03210e8i q^{21} +(1.87382e8 - 1.47575e8i) q^{22} -3.55854e7 q^{23} +(7.09620e8 + 1.54511e9i) q^{24} +7.11027e8 q^{25} +(-2.21016e9 + 1.74064e9i) q^{26} -4.74662e9i q^{27} +(3.37597e8 - 1.40029e9i) q^{28} +1.58717e9i q^{29} +(-2.89914e9 - 3.68115e9i) q^{30} -5.76500e9 q^{31} +(1.17074e9 + 5.96011e9i) q^{32} -6.04306e9 q^{33} +(7.47714e9 + 9.49404e9i) q^{34} +3.96959e9i q^{35} +(7.03533e9 - 2.91813e10i) q^{36} +1.31575e10i q^{37} +(-2.47294e9 + 1.94759e9i) q^{38} +7.12777e10 q^{39} +(-6.98618e9 - 1.52115e10i) q^{40} -2.35463e10 q^{41} +(-2.86705e10 + 2.25798e10i) q^{42} +1.45984e10i q^{43} +(-2.09867e10 - 5.05970e9i) q^{44} +8.27238e10i q^{45} +(1.99278e9 + 2.53032e9i) q^{46} -6.81077e10 q^{47} +(7.01271e10 - 1.36984e11i) q^{48} -6.59721e10 q^{49} +(-3.98175e10 - 5.05580e10i) q^{50} -3.06183e11i q^{51} +(2.47538e11 + 5.96790e10i) q^{52} +1.66280e11i q^{53} +(-3.37511e11 + 2.65811e11i) q^{54} +5.94937e10 q^{55} +(-1.18474e11 + 5.44115e10i) q^{56} +7.97523e10 q^{57} +(1.12857e11 - 8.88815e10i) q^{58} -1.27634e11i q^{59} +(-9.93989e10 + 4.12289e11i) q^{60} -4.24164e11i q^{61} +(3.22840e11 + 4.09924e11i) q^{62} +6.44289e11 q^{63} +(3.58236e11 - 4.17012e11i) q^{64} -7.01726e11 q^{65} +(3.38411e11 + 4.29695e11i) q^{66} +3.76204e11i q^{67} +(2.56359e11 - 1.06333e12i) q^{68} -8.16028e10i q^{69} +(2.82260e11 - 2.22297e11i) q^{70} -1.30947e12 q^{71} +(-2.46893e12 + 1.13390e12i) q^{72} +4.78648e11 q^{73} +(9.35572e11 - 7.36820e11i) q^{74} +1.63049e12i q^{75} +(2.76969e11 + 6.67746e10i) q^{76} -4.63363e11i q^{77} +(-3.99155e12 - 5.06824e12i) q^{78} -3.64547e11 q^{79} +(-6.90399e11 + 1.34860e12i) q^{80} +5.04277e12 q^{81} +(1.31860e12 + 1.67428e12i) q^{82} +8.72792e11i q^{83} +(3.21109e12 + 7.74163e11i) q^{84} +3.01436e12i q^{85} +(1.03803e12 - 8.17509e11i) q^{86} -3.63963e12 q^{87} +(8.15485e11 + 1.77562e12i) q^{88} -1.02458e11 q^{89} +(5.88212e12 - 4.63253e12i) q^{90} +5.46536e12i q^{91} +(6.83240e10 - 2.83396e11i) q^{92} -1.32200e13i q^{93} +(3.81403e12 + 4.84284e12i) q^{94} -7.85158e11 q^{95} +(-1.36674e13 + 2.68468e12i) q^{96} -6.15772e12 q^{97} +(3.69444e12 + 4.69098e12i) q^{98} -9.65621e12i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 112 q^{2} - 3840 q^{4} + 326112 q^{6} - 351664 q^{7} + 1347584 q^{8} - 7328466 q^{9}+O(q^{10}) \) 2 * q - 112 * q^2 - 3840 * q^4 + 326112 * q^6 - 351664 * q^7 + 1347584 * q^8 - 7328466 * q^9	\( 2 q - 112 q^{2} - 3840 q^{4} + 326112 q^{6} - 351664 q^{7} + 1347584 q^{8} - 7328466 q^{9} - 3210560 q^{10} - 36524544 q^{12} + 19693184 q^{14} + 103540560 q^{15} - 119472128 q^{16} - 267040604 q^{17} + 410394096 q^{18} + 359582720 q^{20} + 374763360 q^{22} - 71170832 q^{23} + 1419239424 q^{24} + 1422053450 q^{25} - 4420324288 q^{26} + 675194880 q^{28} - 5798271360 q^{30} - 11530003136 q^{31} + 2341470208 q^{32} - 12086118360 q^{33} + 14954273824 q^{34} + 14070654720 q^{36} - 4945877792 q^{38} + 142555458288 q^{39} - 13972357120 q^{40} - 47092697836 q^{41} - 57340925184 q^{42} - 41973496320 q^{44} + 3985566592 q^{46} - 136215473184 q^{47} + 140254248960 q^{48} - 131944236366 q^{49} - 79634993200 q^{50} + 495076320256 q^{52} - 675022489920 q^{54} + 118987366800 q^{55} - 236948389888 q^{56} + 159504558792 q^{57} + 225713203008 q^{58} - 198797875200 q^{60} + 645680175616 q^{62} + 1288578833712 q^{63} + 716471009280 q^{64} - 1403452961440 q^{65} + 676822628160 q^{66} + 512717959680 q^{68} + 564519185920 q^{70} - 2618943314736 q^{71} - 4937861763072 q^{72} + 957295743828 q^{73} + 1871143798976 q^{74} + 553938312704 q^{76} - 7983105664128 q^{78} - 729094463200 q^{79} - 1380797644800 q^{80} + 10085533401402 q^{81} + 2637191078816 q^{82} + 6422183620608 q^{84} + 2076050806112 q^{86} - 7279250797008 q^{87} + 1630970142720 q^{88} - 204915282700 q^{89} + 11764239900480 q^{90} + 136647997440 q^{92} + 7628066498304 q^{94} - 1570316198960 q^{95} - 27334885244928 q^{96} - 12315434746684 q^{97} + 7388877236496 q^{98}+O(q^{100}) \) 2 * q - 112 * q^2 - 3840 * q^4 + 326112 * q^6 - 351664 * q^7 + 1347584 * q^8 - 7328466 * q^9 - 3210560 * q^10 - 36524544 * q^12 + 19693184 * q^14 + 103540560 * q^15 - 119472128 * q^16 - 267040604 * q^17 + 410394096 * q^18 + 359582720 * q^20 + 374763360 * q^22 - 71170832 * q^23 + 1419239424 * q^24 + 1422053450 * q^25 - 4420324288 * q^26 + 675194880 * q^28 - 5798271360 * q^30 - 11530003136 * q^31 + 2341470208 * q^32 - 12086118360 * q^33 + 14954273824 * q^34 + 14070654720 * q^36 - 4945877792 * q^38 + 142555458288 * q^39 - 13972357120 * q^40 - 47092697836 * q^41 - 57340925184 * q^42 - 41973496320 * q^44 + 3985566592 * q^46 - 136215473184 * q^47 + 140254248960 * q^48 - 131944236366 * q^49 - 79634993200 * q^50 + 495076320256 * q^52 - 675022489920 * q^54 + 118987366800 * q^55 - 236948389888 * q^56 + 159504558792 * q^57 + 225713203008 * q^58 - 198797875200 * q^60 + 645680175616 * q^62 + 1288578833712 * q^63 + 716471009280 * q^64 - 1403452961440 * q^65 + 676822628160 * q^66 + 512717959680 * q^68 + 564519185920 * q^70 - 2618943314736 * q^71 - 4937861763072 * q^72 + 957295743828 * q^73 + 1871143798976 * q^74 + 553938312704 * q^76 - 7983105664128 * q^78 - 729094463200 * q^79 - 1380797644800 * q^80 + 10085533401402 * q^81 + 2637191078816 * q^82 + 6422183620608 * q^84 + 2076050806112 * q^86 - 7279250797008 * q^87 + 1630970142720 * q^88 - 204915282700 * q^89 + 11764239900480 * q^90 + 136647997440 * q^92 + 7628066498304 * q^94 - 1570316198960 * q^95 - 27334885244928 * q^96 - 12315434746684 * q^97 + 7388877236496 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more